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)