“matrix of a linear map”的概念、定义、翻译、参考文献-科学参考

matrix of a linear map

Mathematics

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,…,v_m and w₁,…,w_n, the matrix for T, with respect to these bases, is the n × m matrix that sends the coordinate vector for v (wrt the v_i) to the coordinate vector for Tv (wrt the w_i). Precisely, this means the matrix has entries a_ij, where

$T (v_{i}) = \sum_{j = 1}^{n} a_{j i} w_{j} .$

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

单词	matrix of a linear map
释义	matrix of a linear map Mathematics 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,…,v_m and w₁,…,w_n, the matrix for T, with respect to these bases, is the n × m matrix that sends the coordinate vector for v (wrt the v_i) to the coordinate vector for Tv (wrt the w_i). Precisely, this means the matrix has entries a_ij, where $T (v_{i}) = \sum_{j = 1}^{n} a_{j i} w_{j} .$ Any two matrices representing T will be equivalent. See change of basis, diagonalization.
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