We present a collection of forty-four parametrized test matrices. The matrices are mostly square, dense, nonrandom, and of arbitrary dimension. The collection includes matrices with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involuntary, and totally positive matrices. For each matrix we give a MATLAB M-file that generates it, and for small dimensions, a printout of the matrix, pictures of it, and a plot of its field of values.