# Why do we learn matrix in math

## Matrix calculation - basics

### Special matrices

In the following, some matrices are named which differ from other matrices due to their special shape.

**Square matrices**

Matrices that have the same number of rows and columns (\ (m = n \)) are called quadratic. Well-known representatives of this genus are the 2x2 and 3x3 matrices, which are often found in schools and studies.

\ (A = \ begin {pmatrix} {\ color {red} a_ {11}} & a_ {12} & a_ {13} \ a_ {21} & {\ color {red} a_ {22}} & a_ {23} \ a_ {31} & a_ {32} & {\ color {red} a_ {33}} \ end {pmatrix} \)

The elements of a square matrix, for which \ (i = j \) applies, form the so-called. **Main diagonal** the matrix.

**Zero matrix**

If all elements of a matrix are equal to zero, it is called a zero matrix.

\ (A = \ begin {pmatrix} 0 & 0 \ 0 & 0 \ end {pmatrix} \)

A 2x2 zero matrix is used as an example.

**Identity matrix**

A matrix in which the elements of the main diagonal are equal to one and all other elements are equal to zero is called an identity matrix.

\ (A = \ begin {pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \ end {pmatrix} \)

**Diagonal matrix**

A matrix in which all elements - except the elements of the main diagonal - are equal to zero is called a diagonal matrix.

\ (A = \ begin {pmatrix} 3 & 0 & 0 \ 0 & -4 & 0 \ 0 & 0 & 2 \ end {pmatrix} \)

*Note:* The identity matrix (elements of the main diagonal equal to one) and the zero matrix (elements of the main diagonal equal to zero) are special diagonal matrices.

**Upper triangular matrix**

If all elements below the main diagonal are equal to zero, the matrix is called the "upper triangular matrix".

\ (A = \ begin {pmatrix} {\ color {red} 3} & {\ color {red} 4} & {\ color {red} 1} \ 0 & {\ color {red} -5} & { \ color {red} 4} \ 0 & 0 & {\ color {red} 4} \ end {pmatrix} \)

**Lower triangular matrix**

If all elements above the main diagonal are equal to zero, the matrix is called the "lower triangular matrix".

\ (A = \ begin {pmatrix} {\ color {red} 3} & 0 & 0 \ {\ color {red} 1} & {\ color {red} -2} & 0 \ {\ color {red } 5} & {\ color {red} 5} & {\ color {red} 4} \ end {pmatrix} \)

**More matrices ...**

We have written a separate article for each of the following matrices

As you can see, the topic of matrix calculations is a relatively large sub-area of mathematics. This is mainly due to the great importance of matrices in practice.

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