Glossary of matrix theoryEdit

The terms below are used in the branch of mathematics called matrix theory, which is often considered a subfield of linear algebra. For specific types of matrices, see the List of matrices. For some matrix operations, see Matrix.

A rectangular array of objects which are usually members of a ring.
The definitions below will assume the following matrix:
One of the objects in a matrix.
aij for a specific choice of i and j.
Size or dimensions
The number of rows and columns, respectively, of a matrix; usually expressed in the form m × n, read "m by n".
i-th row of matrix A
j-th column of matrix A
Main diagonal
The elements whose row and column number match.
An operation resulting in a new matrix whose rows are the columns of the original matrix and whose columns are the rows of the original matrix, or the resulting matrix itself.
The sum of the elements on the main diagonal.


The determinant of the matrix obtained by deleting a given row and column from the original matrix.
Note that the i-th row and j-th column are missing in the above determinant.


A matrix with one row (a row vector) or one column (column vector).
See Vector for more information.
Linear transformation
The function that results from multiplying a given matrix by an appropriately sized vector of variables.
The dimension of the space generated by the rows of a given matrix.
The dimension of the image of the linear transformation represented by the matrix.