The Wolfram Language provides a range of methods for representing and constructing matrices. Especially powerful are symbolic representations, in terms of symbolic systems of equations, symbolic sparse or banded matrices, and symbolic geometric transformations.

Table — construct a matrix from an expression

Array — construct a matrix from a function

CoefficientArrays — construct a matrix from a system of equations

SparseArray — construct a sparse matrix from positions and values

Normal — convert a sparse matrix to ordinary form

Band — give values on any collection of bands, for tridiagonal etc. matrices

IdentityMatrix  ▪  DiagonalMatrix  ▪  ConstantArray  ▪  CenterArray

ArrayFlatten — flatten a matrix of matrices to make a block matrix

Partition — partition a list to make a matrix

Join — join several matrices to make a matrix

PadLeft, PadRight — pad out a ragged array to make a matrix

ArrayPad — add padding around a matrix

HilbertMatrix  ▪  HankelMatrix  ▪  ToeplitzMatrix

Geometric Matrices »

RotationMatrix  ▪  ScalingMatrix  ▪  ShearingMatrix  ▪  ...

Structure Matrices »

BoxMatrix  ▪  CrossMatrix  ▪  DiamondMatrix  ▪  DiskMatrix  ▪  GaussianMatrix  ▪  ...