Let T: V -->W be a linear transformation between finite-dimensional vector spaces and let B and C be bases for V and W, respectively. Show that the matrix of T with respect to B and C is unique. That is, if A is a matrix such that A [ v ]B= [ T(v) ]C for all v in V, then A = [ T ]c<--B·
Let T: V -->W be a linear transformation between finite-dimensional vector spaces and let B and C be bases for V and W, respectively. Show that the matrix of T with respect to B and C is unique. That is, if A is a matrix such that A [ v ]B= [ T(v) ]C for all v in V, then A = [ T ]c<--B·
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 43EQ
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Let T: V -->W be a linear transformation between finite-dimensional
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