The main and abstract context is that it is a certain quantity of numbers arranged in a rectangle with certain numbre of rows and columns.
Types of Matrices
Rectangular: arranged as nxm.
Squared arranged as n=m rows and columns. They have symmetry and asymmetry.
Complex: Imaginary matrix. Real: with real numbers.
Operations with matrices
Addition and Substraction: They can just be done with matrices of same dimension, and so you just add or subtract the numbers in the same position.
Multiplication: When multiplying times a number multiply each number of the matrix time the number. When multiplying times another matrix the other matrix has to have the same numbers of rows as the other columns.
Equality: Two matrices A and B of same order mxn are said to be equal if and only if all of their componentsare equal.
Transposition: The columns and rows are changed and that is the transposition.
Scalar multiplication: You multiply every component by the scalar c , mathematically it is written c A d=ef [cai j ] , Division of a matrix by a nonzero scalar c is equivalent tomultiplication by (1/c).
Matrix by Vector product: you multiply as if the matrix was turned to the right, and then add as it is.
Rows of A are multiplied with columns of B and so you obtain C matrix result, that is nxp, because one is mxn and the other nxp.