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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