и потому каждый вектор
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAATCAYAAADiQ08DAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF/SURBVEjH7VZLbsIwEJ3u6QGoMHeA4QjIeAHbShCxosoCoWyolAWqTHY5A6uyK2eAo7QngDM0tZ0PJrVD+pHCIouRpZfE8968mVEgCAK45bhpcjVBa1KAO1tUTnBByVIQ+RQRJaceETrrYeUVXDs4BCAn5vFOioWh22CE7HTsXwiWsclYxRY7uGHY0HGP0scp581CgqYktsSreb9LAI6XNuF7Pkk+JghbQhfLrHLMmZUakrj0Msm5/BlG2F5XrPAcViY4nzYR4APHfCRF8zGOUrKlp1hZgJNtfDqv+edSNUX64vr+/U8tTgRHRYNxlSD3WEdYd7IpS6tgmMKrFkt7pfhU6KCNm6L3jaDqixYcbMoUwfZg82t7tXsdxmZF9xhBj+JTr0feUqVGAWIl9Oer7l/Xi57ThH+bYHmJtFbZTNhO9pnp4ziZsNP3H8r0oMSVvXK95HpX9Pqzae1cEMw2fDIUcZVgLzFbL56nvrgHk54+mns2DluO+mehJlh1fAHNeiXuM+fAgAAAAABJRU5ErkJggg==)
единственным способом представим в виде суммы
![](data:image/png;base64,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)
где
![](data:image/png;base64,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)
Вектор
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzNQVTMQMMIwujhBzdHGDAuACv8xyHjsSevo4AGJNUQb+yDz8TobrJjB+G5sfb0kiN/RkcbjZuxWS5Tm+jwPQ1kG2ZseefWGYH59rKSbW14YUQEGUmzMwHDXOLrBB8TPc3MLg7mCJM3VWS5Gxm55KURHFciPHjIMe2Q9PXtM5DxmovuVsGZZht3AQLuDzblYNcPiEkRHR0d7Ep1IwCEs67EyrT5NEmQrLLCI18zA8JqBQfY1LIrom7aHhmYAPXRugc+sOHcAAAAASUVORK5CYII=)
называют (ортогональной) проекцией вектора
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACbSURBVDjLY2hsbGQgFTMMnCYgYARhfGIoGhqijX2Akv8YGGTfeOTVG6KIyXrsTuvo4MHpvBw32WIG46iFEDp6AVF+qs/zMJRlYHgj65ZTTHRAdHSk8XjIMOwxjm7wIVpTnptxiomJ7AqQEwlqAoUQyOMgZ4GdKOuxMq28nBdkCCxgUDSBPQ0KJajHwU6UZdgNEkP3G8MQS0bEYACqqBXputXHeAAAAABJRU5ErkJggg==)
на подпространство
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACzSURBVDjLY2hsbGQgFzNQXTMQMKJjojXnuMkWAzX8A+L/YFrWY3daRwcP0c5uiDb2YWCQfeORV29Isp/Btst47MFmI17NHR1pPB4yDHtk3XKKSQ6w+jwPQ1kG2Zv4nIw/wAg4GatmmJMZjKMWkhzP9fWxksYMDHeNoxt8SNccaezLwGB8N7a+XhJdHN1AFI3l5Wm8MCcjp67qLBcjWQajU+gGoiUKcKrCjo2jF9A+Y9BFMwA/Xmfw4z1oyAAAAABJRU5ErkJggg==)
и обозначают
![](data:image/png;base64,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)
, а
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB1SURBVCjPY2hsbGQgFTNQRRMQMKJjvJo6OtJ4PGQZdgMV/oPi/wwMsq898uoNcWqqz4tUjcyrV4XZGGXMsNA4usGHKD/h04DTT/g0YGgiRgOKJriGyHpfWKhVh4YaxdbXS+LUlOchW4QUahBsHL2AdpFLM00Av+7lUHvVTnYAAAAASUVORK5CYII=)
- перпендикуляром (ортогональной составляющей) из вектора
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACbSURBVDjLY2hsbGQgFTMMnCYgYARhfGIoGhqijX2Akv8YGGTfeOTVG6KIyXrsTuvo4MHpvBw32WIG46iFEDp6AVF+qs/zMJRlYHgj65ZTTHRAdHSk8XjIMOwxjm7wIVpTnptxiomJ7AqQEwlqAoUQyOMgZ4GdKOuxMq28nBdkCCxgUDSBPQ0KJajHwU6UZdgNEkP3G8MQS0bEYACqqBXputXHeAAAAABJRU5ErkJggg==)
на подпространство
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC2SURBVDjLY2hsbGQgFzNQXTMQMKJjojXnecgWATX8A+L/YFrWY3daRwcP0c5uiDb2YWCQfeORV29Isp9z3GSLGWQ89mCzEa/mjo40Hg8Zhj2ybjnFJAdYfZ6HoSyD7E18TsapmRgnY9UMczKDcdRCkuO5vj5W0piB4a5xdIMP6ZojjX0ZGIzvxtbXS6KLoxuIorG8PI0X5mTk1FWd5WIky2B0Ct1AtEQBTlXYsXH0AtpnDLpoBgBJImfzQM/i8wAAAABJRU5ErkJggg==)
:
![](data:image/png;base64,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)
. Очевидно, что
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. (6)
Если
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
(7)
и тогда
![](data:image/png;base64,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)
.
Умножаем последнее равенство скалярно на
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAZCAYAAADXPsWXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEXSURBVDjLY2hsbGSgFDOMGjIiDQECRnRMkiEgDTlussVA+h8Dg+xrNzfjOgYZjz1pHR08RBlSXp7G6yHDsIfBOHoBiF9fHytpzMBwV9Ytp5hol0QZMyyEGQDCHR1pPCBDjaMbfIgypCHa2IeBwfhubH29JEysOsvFSJbB6BSyGLK3MQyBuCJqIabXEGLIONrYuA5mOKohRlGLQDaUl8dKAcPiDpD93zg6OjUyst4QlyuweAcUIyBsfCeyPtIQYpDxHWTvgMNJlmE3cjiRlbjqIz3sPPIQriPLkGgPj2TkdEO6K/I8DGWNo3rJyjuwwASlZvR0Q5QBoMB0M3arTatPk/SQM5mJnm6IDwdjhgWgvIQcoMO0UAIA4QxjRO2E2t8AAAAASUVORK5CYII=)
,
![](data:image/png;base64,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)
, с учетом
![](data:image/png;base64,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)
, получаем
![](data:image/png;base64,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)
(8)
Эта система в силу существования представления (7) совместна. Определитель матрицы этой системы есть определитель Грама
![](data:image/png;base64,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)
. Если
![](data:image/png;base64,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)
- линейно независима, то
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAbCAYAAABRLYBiAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAPFSURBVGje7VmxbtswEGX3+ANihP0Hi3M7GaoKJGsBWfBU10MQaEgCaAhixZuH5gc62WN+oc4X5A8KOF8Qf0NdkRQlmiIZSqIbu+VwMCzTp+O9u3d3JJhOp8DJ/yXOCQ50Jw50Jw50I4UAvHOO3W8fWVWWJMMuQlHqgNVLhNBkmCTdvQQdR6QoqkhN0+ExAujnME2PHbB6KXy1A+BFrGqBjv80QGCRff4uBA0WSTLu+Mi/Hc9mR0L0pg7wmsDvgBUvfHjF8EJhemYMehqiM/JHGCx5cO8idIqfQ//iil9/c973IBrcOzDryQDB+/75jWctkAhuaIWTj7IJWMmAVwG+QdHdqSqSxN8wI6jWO1ELSaKMPW00gbPZ+Cg4AY88DkT/SfAosjKoZCwAa4CiueqlsY9GQZz2eJryAHzin5n2Bm1rVltdu6ijdWxK46AHgfdkWhYJsBA+yHxNdcFfW9hInlVApzUcPYtG6Db1muF4bVln4Ivvo1tZ9Jk615Yum4ALNk1MbdIljMzn2Xuus9J6LQssWnq3scsp/llk4Qo9iAbT6ALLvDnY0E9aN1QvK0e4cYfozJmDGSH2BGbjoD1d9kbUdjapQCGMGsDLrSa68D1rqrfZuBHobIGqxuRN3EbckA50whyccbK6Y9702NNlrxFrZ5MOdNm7dOukoBMWBuvGoFMKq4KrAl32nPYMtBTUqX2v6TKdT603YYY2NQGd3w/RC4OHcZJ0VPtsXNMjBOZZXVqLY0RB/ZKAUIFOs6BcX1LhYFGWDDlDyDNKrotz3ko2Tu42y9U2sT3q7KlB7xuB6iv0zt7Hj2gkUYWxuwJ66bwMjCTpbkWahCZ00cScgv9PjmcpKNkoGH0Lw7SHjfz0Hv1QNY11dMW+/4XNph7wlrxOmT7xWd3vJjbR8Tf4iP2iynaTyYeM0JppqpKAuCfLGIHZJGWRqfRsGGe8EFmSiNEZzg5yWOMXpmEvDyjSBMpAz2vQC98omugSDzyYLTJ9Bcvk+3ntexubyCnlEI1wV68es9STT5OjbZ4hVD2ApQsEMK/bUOkynWVII1uC4CsfnG31NdWB9+f74SiKos/6wxmzLLY6Zlo5/sMRW/MYVprprLw0dAR2Ih98bfW10cEYQlfTeVY6ONBptsPvdTaAGx8CuoWbJpqJuPbRGrsPR6z45LIfxx/I5VRWY6XBhKLJmxwo2VLEbo1MnV70DYpeoZaDhYOMfbgHIHfmGYuRfQosgX30lreSO7hA+Ps16tCkSQ+0t6A7OQxxTnCgO3GgO/kn5Q/6QPZU5JBVUwAAAABJRU5ErkJggg==)
и система (8) имеет единственное решение. В противном случае у системы (8) решений бесконечно много. Но нам достаточно найти одно (все другие решения дадут нам те же векторы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzNQVTMQMMIwujhBzdHGDAuACv8xyHjsSevo4AGJNUQb+yDz8TobrJjB+G5sfb0kiN/RkcbjZuxWS5Tm+jwPQ1kG2ZseefWGYH59rKSbW14YUQEGUmzMwHDXOLrBB8TPc3MLg7mCJM3VWS5Gxm55KURHFciPHjIMe2Q9PXtM5DxmovuVsGZZht3AQLuDzblYNcPiEkRHR0d7Ep1IwCEs67EyrT5NEmQrLLCI18zA8JqBQfY1LIrom7aHhmYAPXRugc+sOHcAAAAASUVORK5CYII=)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB1SURBVCjPY2hsbGQgFTNQRRMQMKJjvJo6OtJ4PGQZdgMV/oPi/wwMsq898uoNcWqqz4tUjcyrV4XZGGXMsNA4usGHKD/h04DTT/g0YGgiRgOKJriGyHpfWKhVh4YaxdbXS+LUlOchW4QUahBsHL2AdpFLM00Av+7lUHvVTnYAAAAASUVORK5CYII=)
). Если система (8) получилась несовместной, ищите ошибку. Вычисления сокращаются, если известны базисы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC2SURBVDjLY2hsbGQgFzNQXTMQMKJjojXnecgWATX8A+L/YFrWY3daRwcP0c5uiDb2YWCQfeORV29Isp9z3GSLGWQ89mCzEa/mjo40Hg8Zhj2ybjnFJAdYfZ6HoSyD7E18TsapmRgnY9UMczKDcdRCkuO5vj5W0piB4a5xdIMP6ZojjX0ZGIzvxtbXS6KLoxuIorG8PI0X5mTk1FWd5WIky2B0Ct1AtEQBTlXYsXH0AtpnDLpoBgBJImfzQM/i8wAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAYAAACNiR0NAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADVSURBVDjLY2hsbGSgJmYYNZBoHO3hkZzW0cFDtIFAwIiMKTIwx022GGjIPyD+D6ZlPXajaybZhQ3Rxj4MDLJvPPLqDaniZbArZTz2IGtCDoJIN7eUtPJyXvTgwGpYR0caj4cMwx5Zt5xiFDFZht3QoEDByOqwGlif52EoyyB7E5d3SU422LxLtoEw7zIYRy2kSsKur4+VNGZguGsc3eBDFQMhycX4bmx9vSS6ODGWoHDKy9N4Yd5FTiLVWS5GsgxGp9AtwWsgxGWYSQKOjaMXjJaHWDEAOe06PqVsPnwAAAAASUVORK5CYII=)
и если, опираясь на соотношения (6), выбрать то подпространство, размерность которого меньше.
Умение находить
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
позволит успешно справиться с большинством задач на вычисление длин, расстояний и углов.
Задача 2.3. Вычислить расстояние от вектора
![](data:image/png;base64,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)
до плоскости
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADbSURBVDjLzZNBCoMwEEWney+gmEPI3EGysAeoIVtX4qIKWUZ3OYbew4t04Q16htqoGwkxTaEtDQyBR3jwZybQdR18quDrMn1OZrm4U8YQev3woWtebkKrq4u/jFmmpAYgd1rJxIc7ZTnCAJgPvvxQJiUPEWBC1mY+3ClrGWYAOHEhon2z5QXPK5cy9JatUbZGmzUfRbTKlCoCGsNI0rJ+J6JVJiuaECA3c1pbdPsUD2V69A3EdCyUCny4VbY0WAgeLVF0xGa/9TbulG3LuGs2st7Gza3/7Uf/C9kTlXm3FqepImkAAAAASUVORK5CYII=)
, заданной системой уравнений
![](data:image/png;base64,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)
.
Решение. Напомним: плоскостью (линейным многообразием) называется множество векторов вида
![](data:image/png;base64,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)
,
где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAYCAYAAAAcYhYyAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGSgFDOMGjLiDAECRhAmJIbTkIZoYx+g4n8MDLKvXbKqjUAa4WKyHrvTOjp4iPZOjptsMYNx1EIIHb2ArDCpz/MwlGVgeCPrllNMdsCWl6fxesgw7DGObvDBFjYYYYbNkDw34xQTE9nlIC8hawZ7Dxg+6C7EsAUUkLIeeUVgL8l6rEwrL+cFGeoW75YoaxzVC1IbZSzb65FXb4hhSJ6HbBE4FqAB2dGRxuMhy7AbbDPQUJArYN4DW4TkGqITFMg1MNtBrjR2y0sh2RCquAQcRsAwAYUbzjAhBkcbMyyAhdFoeYIfAwANAEWw/JD+tQAAAABJRU5ErkJggg==)
- вектор сдвига,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC2SURBVDjLY2hsbGQgFzNQXTMQMKJjojXnecgWATX8A+L/YFrWY3daRwcP0c5uiDb2YWCQfeORV29Isp9z3GSLGWQ89mCzEa/mjo40Hg8Zhj2ybjnFJAdYfZ6HoSyD7E18TsapmRgnY9UMczKDcdRCkuO5vj5W0piB4a5xdIMP6ZojjX0ZGIzvxtbXS6KLoxuIorG8PI0X5mTk1FWd5WIky2B0Ct1AtEQBTlXYsXH0AtpnDLpoBgBJImfzQM/i8wAAAABJRU5ErkJggg==)
- данное (направляющее) подпространство. Любая плоскость может быть задана как множество решений некоторой системы линейных уравнений. Частное решение этой системы дает координаты вектора сдвига. Общее решение приведенной системы - направляющее подпространство. Учитывая это, находим, что
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
.
Расстояние от вектора
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACiSURBVDjLY2hsbGQgFTMMnCYgYARhfGIoGhqijX2Akv8YGGRfu2RVG4EUwsVkPXandXTw4HRejptsMYNx1EIIHb2AKD/V53kYyjIwvJF1yykmOiA6OtJ4PGQY9hhHN/gQrSnPzTjFxER2OciJeDXBQgjkcVmPvCKwE2U9VqaVl/OCDPHIqzfE0JTnIVsEDiWox8FOlGXYDRIDGTJIUgTNNAEAhcoS4cBY+HgAAAAASUVORK5CYII=)
до плоскости
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADcSURBVDjLzZNBCoMwEEWney+gmEPI3EGysAeowa0ryUKFLKO7HEPv4UW68AY9Q23UjZWYptCWBobAIzz4MxNo2xY+VfB1mT6nfdm4VcYQOv3wrmuab0J5aeMvYxYxqQDIjXIZuXCrLEXoAdPelR/KpMx8BBiRNYkLt8oahgkAjpkQwbbZ8oLnhUvpO8uWKGuj9zUdRTTKlMo9GsJA4qJ6J6JRJjmNCJDrflprdPMUD2V69DWEdMiV8ly4UTY3WIgsmKPoiPV2603cKuOUlE/NRtaZ+H7rf/vR/0L2AJw1txyixfYGAAAAAElFTkSuQmCC)
определяется как
![](data:image/png;base64,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)
или как
![](data:image/png;base64,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)
.
Так как
![](data:image/png;base64,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)
(применена теорема Пифагора), то
![](data:image/png;base64,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)
Мы получили формулу
![](data:image/png;base64,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)
Остается вычислить
![](data:image/png;base64,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)
и его длину.
![](data:image/png;base64,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)
.
![](data:image/png;base64,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)
и тогда
![](data:image/png;base64,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)
.
Умножаем последнее равенство скалярно на
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
, с учетом
![](data:image/png;base64,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)
, получаем
![](data:image/png;base64,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)
Решая систему, находим
![](data:image/png;base64,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)
.
Тогда
![](data:image/png;base64,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)
.
![](data:image/png;base64,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)
.
![](data:image/png;base64,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)
3. ОПЕРАТОРЫ В ЛИНЕЙНЫХ ПРОСТРАНСТВАХ.
Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADGSURBVDjLY2hsbGQgFzNQRTMQMCJjXGJYNed5yBYBFfwD4v8g2ji6wQdJ7B+DcfQCvM6uz/MwlGUwOhVbXy8JN9TNOMUjr96QoJ87OtJ4PGQY9oBsBfEboo19ZD3yiogOsChjhoUMxlELy8vTeD08opNJCm2QbQwMxnfd3IxrcTkXp2aIvxneyLrlFJMczzlussUgm5EDjWQ/k5zC6utjJY0ZGO7CQpukFAZ0cgkDg+wbl6xqI6I1Q228A09N0BRGn4xBd80AC0FmfNIluGMAAAAASUVORK5CYII=)
- два произвольных линейных пространства. Как известно, оператором, действующим из
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADGSURBVDjLY2hsbGQgFzNQRTMQMCJjXGJYNed5yBYBFfwD4v8g2ji6wQdJ7B+DcfQCvM6uz/MwlGUwOhVbXy8JN9TNOMUjr96QoJ87OtJ4PGQY9oBsBfEboo19ZD3yiogOsChjhoUMxlELy8vTeD08opNJCm2QbQwMxnfd3IxrcTkXp2aIvxneyLrlFJMczzlussUgm5EDjWQ/k5zC6utjJY0ZGO7CQpukFAZ0cgkDg+wbl6xqI6I1Q228A09N0BRGn4xBd80AC0FmfNIluGMAAAAASUVORK5CYII=)
называется отображение пространства
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
в пространство
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzNQRTMQMCJjXGJYNee4yRYDFfwD4v8g2ji6wQdJ7B+DcfQCvM6uz/MwlGUwOhVbXy8JE8tzM07xyKs3JOjnjo40Hg8Zhj0gW0H8hmhjH1mPvCKiAyzKmGEhg3HUwvLyNF4Pj+hkkkIbZBsDg/FdNzfjWlzOxakZ4m+GN7JuOcUkxzMkhI3vIgcayX4mOYWVl8dKGTMw3IWFNkkpDOjkEgYG2TcuWdVGRGuur4+VBNp4B56aoCmMPhmD7poB4vRmZ8/GlXIAAAAASUVORK5CYII=)
. Если отображение обозначить символом
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGSgBDMMLQOqs1yMjN3yUsgyoLw8jddDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTKgPs/DUNY4ugdkCAOD8d3Y+npJog0A+dvN2K0urbyctz7S2JdkA6D+/gfF/xlkPPakdXTwEGUA2N9IAQY2jFgDQPEN8jeGa4yjFuJNSEDACPYryCagv9HTgKxbTglIDVYD6utjJY0ZGO7A/CzrkVcE8wpSOPxjkPXYjeyNIZaZsGEAGdaJGLSJSn4AAAAASUVORK5CYII=)
, то это записывают так:
![](data:image/png;base64,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)
.
Образ вектора
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACiSURBVDjLY2hsbGQgFTMMnCYgYARhfGIoGhqijX2Akv8YGGRfu2RVG4EUwsVkPXandXTw4HRejptsMYNx1EIIHb2AKD/V53kYyjIwvJF1yykmOiA6OtJ4PGQY9hhHN/gQrSnPzTjFxER2OciJeDXBQgjkcVmPvCKwE2U9VqaVl/OCDPHIqzfE0JTnIVsEDiWox8FOlGXYDRIDGTJIUgTNNAEAhcoS4cBY+HgAAAAASUVORK5CYII=)
обозначают
![](data:image/png;base64,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)
или
![](data:image/png;base64,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)
и называют значением оператора
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADHSURBVDjLY2hsbGSgBDMMLQOqs1yMjN3yUsgyoLw8jddDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTKgPs/DUNY4ugdkCAOD8d3Y+npJog0A+dvN2K0urbyctz7S2JdkA6D+/gfF/xlkPPakdXTwEGUA2N9IAQY2jFgDQPEN8jeGa4yjFuJNSEDACPYrmk2wNCDrllMCUoPVgPr6WEljBoY7MD/LeuQVwbyCFA7/GGQ9diMbPsQyEzYMAEBSiTlCp4U5AAAAAElFTkSuQmCC)
на векторе
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACnSURBVDjLY2hsbGQgFTMMnCYgYARhfGIoGhqijX2Akv8YGGRfu2RVG4EU1kca+4LFZD12p3V08OB0Xo6bbDGDcdRCCB29gCg/1ed5GMoyMLyRdcspJjogysvTeD1kGPYYRzf4EK0pz804xcREdjnIiXg1wUIIFBiyHnlFYCfKeqxMKy/nBRnikVdviKEJ7GlQKEE93tGRxuMhy7AbJAYyZJCkCJppAgBKlxK7lMR0CAAAAABJRU5ErkJggg==)
. По определению
![](data:image/png;base64,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)
.
Оператор
![](data:image/png;base64,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)
называют
линейным оператором, если
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzNQRTMQMCJjXGJYNee4yRYDFfwD4v8g2ji6wQdJ7B+DcfQCvM6uz/MwlGUwOhVbXy8JE8tzM07xyKs3JOjnjo40Hg8Zhj0gW0H8hmhjH1mPvCKiAyzKmGEhg3HUwvLyNF4Pj+hkkkIbZBsDg/FdNzfjWlzOxakZ4m+GN7JuOcUkxzMkhI3vIgcayX4mOYWVl8dKGTMw3IWFNkkpDOjkEgYG2TcuWdVGRGuur4+VBNp4B56aoCmMPhmD7poB4vRmZ8/GlXIAAAAASUVORK5CYII=)
- пространства над одним и тем же полем
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACeSURBVDjLY2hsbGQgFzNQTTMQMOLCeDV3dKTxeMgy7AYq/AfE/6E0BBtHLcRmAIZpDdHGPgwMsm888uoNEXygYTIee9I6OnhI0gzCUcYMC9HFiNac4yZbDLLdOLrBhxzNJSRpdsmqNgIFUnWWi5EsA8MbBlmP3UT6GS20sWgk2tlEpzCyNYP8WB9p7IvsZ6I0o6UwaMqKXkCfjEFXzQB5OF3InlW8WAAAAABJRU5ErkJggg==)
и при этом
1.
![](data:image/png;base64,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)
(аддитивность оператора);
2.
![](data:image/png;base64,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)
(однородность оператора).
Понятие линейного оператора является одним из важнейших в математике. Это подтверждается хотя бы тем, что основные операторы, изучаемые в математическом анализе и алгебре (предельный переход, дифференцирование, интегрирование, проектирование на подпространство, умножение на матрицу и др.) являются линейными.
Оператор
![](data:image/png;base64,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)
называют также преобразованием пространства
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADnSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzHTbYYqPgfEP8H0cbRDT5I4v8hcrKvPfLqDYnyZkO0sQ9QwxtkDeXlsVLGDAx3ZD3yikgKs46ONB4PGYY9sm45xRCD0ng95ExmxtbXS5IVAWBvyXjsSatPk/SUlV2B7EqSDYN4FRRGqOFDlmHQMLoLiwCyDYMYZLzLyIhhN4Nx1EKyDYMZBApsSHIwvosr4PEahmwQiF+f52EoyyB7k6QwA6Xo+khjX3RXgJMEJImUoKd6rIbV18dKghIjNNX/gyVKdHF8scow9EoNcjAAh7zGVVhoTpgAAAAASUVORK5CYII=)
.
Основные типы задач по этой теме:
a) проверка линейности заданного оператора;