Matrix Addition and Multiplication »

Square matrix:

If a matrix A has n rows and n columns then it can be said that it's a square matrix.

Example 1:

A = \left( {} \right)

Diagonal matrix

A diagonal matrix is a square matrix with all non-diagonal elements being 0. The diagonal matrix is completely denoted by the diagonal elements.

Example 2:

A = \left( {} \right)

The matrix is denoted by the diagonal $(1 , 5 , 9)$

Row matrix

A matrix with one row is called the row matrix

Example 3:

A = \left[ {} \right]

Column matrix

A matrix with one column is called the column matrix

Example 4:

A = \left[ {} \right]

Matrices of the same kind

Matrix $A$ and $B$ are of the same kind if $A$ has as many rows and as many columns as $B$

The transpose of a matrix

The $n \times m$ matrix $A_T$ is the transpose of the $m \times n$ matrix $A$ if and only if the ith row of $A$ is equal to the ith column of $A_T$ for $(i = 1,2,3,..n)$.

Example 5:

A = \left[ {} \right] \to {A^T} = \left[ {} \right]

0-matrix

When all the elements of a matrix $A$ are 0, we call it the 0-matrix.

Example 6:

A = \left[ {} \right]

An identity matrix $I$

An identity matrix $I$ is a diagonal matrix with all diagonal element equal to 1

Example 7:

A = \left[ {} \right]

The opposite matrix of a matrix

If the sign of all the elements of a matrix $A$ are changed, that matrix is the opposite matrix $-A$.

Example 8:

A = \left( {} \right) \to A' = \left( {} \right)

A symmetric matrix

A square matrix is called symmetric if it is equal to its transpose.

Example 9:

A = \left( {} \right)