In mathematics, a matrix is a two dimensional rectangular array of numbers. Matrices play an extremely important role in many areas of mathematics, particularly linear algebra. They are a compact way of representing any linear dependence of some numbers on some other numbers.
Matrix of elements [entries in the two dimensional array] that may be real, integers or complex.
Matrix as a stalking horse, under choice of vector bases, for a linear operator.
Matrices as abbreviation for sets of simultaneous linear equations.
Matrix equality, addition, subtraction, multiplication, division [multiplication by the inverse].
Matrix conformability for multiplication.
Matrix multiplication is generally non-commutative - changing the order in which the matrices are multiplied gives a different product matrix.
Matrix inversion of non-singular matrices.
Gaussian elimination for systems of linear simultaneous equations.
Gauss-Jordan solution for a system of linear simultaneous equations.
Complex matrices; Hermitian, unitary.