Matrix  - A table of related numbers composed of rows and columns. Each number in matrix is referred to as an element. Matrices can represent the coefficients of systems of equations, or variables measured on multiple samples.

Matrix dimensions - These define the number of rows and columns in a matrix.  A 2 x 2 matrix has two rows and two columns.  A 5 x 3 matrix has five rows and three columns.

Transpose - To re-arrange a matrix by switching its rows with its columns. Thus the transpose of the 2 x 3 matrix is a 3 x 2 matrix.

Rank - The rank of a matrix is the column size of the smallest matrix by which it can be post-multiplied when being factored into two matrices. The rank is less than or equal to the total number of columns in the original matrix.

Eigenvalues - The roots of a system of equations or matrix.

Eigenvectors - A vector associate with the root or eigenvalue of a system of equations or matrix that defines a solution associated with that root.

Singular values - The square roots of the eigenvalues of a matrix.

Special matrices

Diagonal matrix - A matrix that has non-zero elements in the major diagonal only. For example a 2 x 2 diagonal matrix is given by:
 

Identity matrix - A square diagonal matrix whose elements are 0 in all cases, except for along the major diagonal. For example, the 2 x 2 identity matrix is:
 

Orthogonal matrix - A special type of matrix that yields the identity matrix when pre-multiplied by its transpose. This means that the columns of the matrix hold independent information.