“matrix of a linear map”的概念、定义、习题解题方法及翻译-数学辞典

单词

matrix of a linear map

释义

matrix of a linear map

A linear map T:V → W between finite-dimensional vector spaces can be represented by a matrix if bases are chosen for V and W. Given bases v1,…,vm and w1,…,wn, the matrix for T, with respect to these bases, is the n × m matrix that sends the coordinate vector for v (wrt the vi) to the coordinate vector for Tv (wrt the wi). Precisely, this means the matrix has entries aij, where

Any two matrices representing T will be equivalent. See change of basis, diagonalization.

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