
Definitions
 Two matrices A and B of the same order whose corresponding entries are equivalent are considered equal. That is: a_{ij}=b_{ij} i=1,...,n ; j=1,2,...,m.
 A square matrix is a matrix which has the same number of rows and columns.
 The main diagonal of a matrix is formed by the elements of a matrix starting in the upper left corner and proceeding down and to the right (a_{ii}).
 A matrix with allzero entries below the toplefttolowerright diagonal is called upper triangular.
 A matrix with allzero entries over the toplefttolowerright diagonal is called lower triangular.
 A matrix with nonzero entries only on the diagonal is called diagonal.
 A diagonal matrix whose nonzero entries are all 1's is called an identity matrix.
The 3 × 3 identity is denoted by I_{3} (pronounced as "eyethree" or "eyesubthree"); similarly, the 4 × 4 identity is I_{4} and the 5 × 5 identity matrix is I_{5}.
 The transpose of a Matrix A is a matrix which is formed by turning all the rows of the given matrix into columns and viceversa. The transpose of matrix A is written A^{T}.
Matrix with only one row

Matrix with only one column

Upper triangular

Lower diagonal

Diagonal






