The Basics of linear algebraEdit
A matrix is composed of a rectangular array of numbers arranged in rows and columns. The horizontal lines are called rows and the vertical lines are called columns. The individual items in a matrix are called elements. The element in the ith row and the jth column of a matrix is referred to as the i,j, (i,j), or (i,j)th element of the matrix. To specify the size of a matrix, a matrix with m rows and n columns is called an mbyn matrix, and m and n are called its dimensions.
Basic operation^{[1]}Edit
Operation  Definition  Example 

Addition  The sum A+B of two mbyn matrices A and B is calculated entrywise:


Scalar multiplication  The scalar multiplication cA of a matrix A and a number c (also called a scalar in the parlance of abstract algebra) is given by multiplying every entry of A by c:


Transpose  The transpose of an mbyn matrix A is the nbym matrix A^{T} (also denoted A^{tr} or ^{t}A) formed by turning rows into columns and vice versa:

Practice problemsEdit
(1)
(2)
(3)
Matrix multiplicationEdit
Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix. If A is an mbyn matrix and B is an nbyp matrix, then their matrix product AB is the mbyp matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B^{[2]}
 ^{[3]}
ExampleEdit
Practice ProblemsEdit
(1)
(2)
Dot productEdit
A row vector is a 1 × m matrix, while a column vector is a m × 1 matrix.
Suppose A is row vector and B is column vector, then the dot product is defined as follows;
or
Suppose and The dot product is
ExampleEdit
Suppose and
Practice problemsEdit
(1) and
(2) and
Cross productEdit
Cross product is defined as follows:
Or, using detriment,
where is unit vector.
ReferenceEdit
 ↑ Sourced from Matrix (mathematics), Wikipedia, 28th March 2013.
 ↑ Sourced from Matrix (mathematics), Wikipedia, 30th March 2013.
 ↑ Sourced from Matrix (mathematics), Wikipedia, 30th March 2013.