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Mathematics
Linear and Abstract Algebra
Matrix Representation of Linear Transformation
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[QUOTE="fresh_42, post: 5461181, member: 572553"] This is how ##A## is defined: ("Define ##A## to be ...") the images of basis vectors of ##V## under the transformation ##T## expressed in coordinates of ##C## with respect to the given bases in ##C## as column vectors of ##A##. The author then shows that the so defined ##A## describes / is in accordance to / concurs / fully determines (whatever) the entire transformation ##T##, as it maps [B]any vector ##v## [/B]when expressed in the coordinates of ##V## with respect to the basis ##\mathit{B}## (RHS) onto the image ##T(v)## expressed in the coordinates of ##W## with respect to the basis ##\mathit{C}## (LHS). EDIT: For short: The matrix ##A## of ##T## can be written as all images of basis vectors of ##V## arranged in columns. [/QUOTE]
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Linear and Abstract Algebra
Matrix Representation of Linear Transformation
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