Definitions

List of matrices

This page lists some important classes of matrices used in mathematics, science and engineering:

Constant matrices

The list below comprises matrices whose elements are constant for any given dimension (size) of matrix.

• Exchange matrix — a binary matrix with ones on the anti-diagonal, and zeroes everywhere else.
• Hilbert matrix — a Hankel matrix with elements Hij = (i + j − 1)−1.
• Identity matrix — a square diagonal matrix, with all entries on the main diagonal equal to 1, and the rest 0.
• Lehmer matrix — a positive, symmetric matrix whose elements aij are given by min(i,j) ÷ max(i,j).
• Pascal matrix — a matrix containing the entries of Pascal's triangle.
• Pauli matrices — a set of three 2 × 2 complex Hermitian and unitary matrices. When combined with the I2 identity matrix, they form an orthogonal basis for the 2 × 2 complex Hermitian matrices.
• Shift matrix — a matrix with ones on the superdiagonal or subdiagonal and zeroes elsewhere. Multiplication by it 'shifts' matrix elements by one position.
• Zero matrix — a matrix with all entries equal to zero.
• Matrix of ones — a matrix with all entries equal to one

Matrices used in statistics

The following matrices find their main application in statistics and probability theory.

Matrices used in graph theory

The following matrices find their main application in graph and network theory.

Other matrix-related terms and definitions

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