Types of matrices

• Square matrix
• Zero matrix
• Vector line
• Vector column
• Diagonal matrix
• Identity matrix
• Upper triangular matrix
• Lower triangular matrix
• Row echelon form

A square matrix is a matrix in which the number of rows equals the number of columns (size n×n), the number n, is called the order of the matrix.

	4	1	-7		- a square matrix with size 3×3
	-1	0	2
	4	6	7

The zero matrix is a matrix whose entries are equal to zero, ie, a_ij = 0, ∀i, j.

	0	0	0		- zero matrix
	0	0	0

Row vector is a matrix consisting of a one row.

1

4

-5

- row vector

Column vector is a matrix consisting of a one column.

	8		- column vector
	-7
	3

Diagonal matrix is a square matrix whose entries standing outside the main diagonal are equal zero.

	4	0	0		- diagonal entries are arbitrarynot diagonal entries are equal to zero
	0	5	0
	0	0	0

Identity matrix is a diagonal matrix in which all the elements on the main diagonal are equal to 1.

The identity matrix usually denoted by I.

I =		1	0	0		- diagonal entries are equal to 1not diagonal entries are equal to 0
		0	1	0
		0	0	1

Upper triangular matrix is a matrix whose elements below the main diagonal are equal to zero.

	7	-6	0
	0	1	6
	0	0	0

Lower triangular matrix is a matrix whose elements above the main diagonal are equal to zero.

	7	0	0
	6	1	0
	-2	0	5

Specifically, a matrix is in row echelon form if:

• all nonzero rows are above all zero rows;
• if the first non-zero element of a row is located in a column with the number i, and the next line is not zero, then the first non-zero element of the next line should be in the column with number greater than i.

7   0   8   0   0   4

7   0   8   8   8   0   0   1   3   5   0   0   0   -3   5   0   0   0   0   0   0   0   0   0   0