Discover Linear Algebra

Section 45.2 Terminology and notation

matrix of a linear transformation $\funcdef{T}{V}{W}$ (relative to bases $\basisfont{B},\basisfont{B}'$ of $V,W$)

the standard matrix of the composition $\invcoordmap{B} T \coordmap{B'}\text{,}$ which is a transformation $\R^n \to \R^m$ in the real case or a transformation $\C^n \to \C^m$ in the complex case, and where $n = \dim V$ and $m = \dim W$

$\matrixOf{T}{B'B}$

notation for the matrix of a linear transformation $\funcdef{T}{V}{W}$ relative to the bases $\basisfont{B}$ of $V$ and $\basisfont{B}'$ of $W$

$\matrixOf{T}{B}$

notation for the matrix of a linear operator $\funcdef{T}{V}{V}$ relative to a single basis $\basisfont{B}$ of $V$

$T^\ell$

notation for composition of $\abs{\ell}$ copies of either $T$ ($\ell$ positive) or $\inv{T}$ ($\ell$ negative)