Types of Matrices

1) An n x n matrix is called a square matrix of order n.

2) An n x m matrix is called a rectangular matrix of order n x m.

3) A matrix whose all entries are zero is called zero matrix (null-matrix).

4) An n x m matrix whose main diagonal (from upper left to lower right) has all elements 1 while all the other elements are 0 is called an identity matrix, and is denoted by I _{n x m}.

A square matrix is called a diagonal matrix if all entries that are not on the main diagonal are zero.

5) In a square matrix, either upper left or lower right part of the main diagonal has all elements are zero is called a triangular matrix.

6) a zero matrix or null matrix is a matrix with all its entries being zero. Some examples of zero matrices are

Definition 5. Matrices of the same size are equal if their respective elements are equal. Two matrices of the same size can be added (elementwise):

.

Any matrix can be multiplied by any number l (all elements of the matrix should be multiplied by this number):

.

Subtraction is defined as

А–В=А +(– 1) В.

Two matrices can be multiplied only if the number of columns in the first matrix equals the number of rows in the second matrix. An matrix is multiplied by an matrix as follows:

We obtain a matrix of size .

Multiplication of matrices is not commutative, and sometimes even impossible:

АВ¹ВА.

Поиск по сайту: