Matrix

Matrices

Definitions

A matrix is a set of real or complex numbers (or element) arranged in rows and columns to form a rectangular array.
A matrix having m rows and n columns is called an m×n matrix and is referred to as having order m×n.
A matrix is indicated by writing the array within large square brackets.

[?(a_11&?(a_12&a_13 )@a_21&?(a_22&a_23 ))] is a matrix of order 2×3,i.e.2 rows and 3 columns

[?(a_(11 )&a_(12 )&a_(13 )@a_(21 )&a_(22 )&a_(23 )@a_(31 )&a_(32 )&a_(33 ) )] is a matrix of order 3×3,i.e.3 rows and 3 columns
Where
a_(11 ) indicates the element in the first row and first column
a_12 indicates the element in the first row and second column
a_13 indicates the element in the first row and third column
a_(21 ) indicates the element in the second row and first column
a_22 indicates the element in the second row and second column
a_23 indicates the element in the second row and third column
a_31 indicates the element in the third row and first column
a_32 indicates the element in the third row and second column
a_(33 ) indicates the element in the third row and third column
Special Matrices

Line matrix: Line matrix consists of one row only.
Example: [?(1&3&5)]

Column matrix: Column matrix consists of one column only.
Example: [?(2@6@4)]

Square matrix: Square matrix is a matrix of order m×m.
Example: [?(1&2&5@6&8&9@1&7&4)]

Diagonal matrix: Diagonal matrix is a square matrix with all elements zero except those on the leading diagonal.
Example: [?(1&0&0@0&3&0@0&0&7)]

Unit matrix: Unit matrix is a diagonal matrix in which the elements on the leading diagonal are all unity.
Example: [?(1&0&0@0&1&0@0&0&1)]
The unit matrix is denoted by I.
Addition and subtraction of matrices
To be added or subtracted two matrices must be of the same order. The sum or difference is then determined by adding or subtracting correspond elements.