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Answers for “为什么在应用矩阵变换之前要将列向量重写为标准基向量的形式?”

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The j-th column of the composed matrix A∘BA \circ B is the image under A of the j-th column of B. To find a missing column, identify the corresponding column in B, treat it as an input vector, and apply the transformation A to it.

Conditions: A is a linear transformation represented by a matrix.; Columns are read as vectors in the domain of A.