InvertibleLinearTransformation 2002-02-13 16:35:42 2005-07-07 23:33:33 Definition invertible % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here An invertible linear transformation is a linear transformation $T: V \longrightarrow W$ which is a bijection. If $V$ and $W$ are finite dimensional, the linear transformation $T$ is invertible if and only if the matrix of $T$ is not singular.