In this tutorial, we will introduce diagonal matrice, upper and lower triangular matrice in Linear Algebra for beginners.
Diagonal Matrice
A diagonal matrix is a square matrix with zero entries except possibly on the main diagonal (extends from the upper left corner to the lower right corner).
We can find:
- A diagonal matrix is a square matrix
- Only elements on the main diagonal are not zero
It can be viewed as:
Here are some examples:
The power of Diagonal Matrice
The power of a diagonal matrice can be defined as:
The inverse of Diagonal Matrice
The inverse of a diagonal matrice can be defined as:
Upper and Lower Triangular Matrice
An upper triangular matrix is a square matrix in which all entries below the main diagonal are zero (only nonzero entries are found above the main diagonal – in the upper triangle).
A lower triangular matrix is a square matrix in which all entries above the main diagonal are zero (only nonzero entries are found below the main diagonal – in the lower triangle).
Here is an example:
Properties
As to upper and lower triangular matrice, there are three properties, they are:
