What is triangular matrix?

A triangular matrix is a special type of square matrix where all the entries above or below the main diagonal are zero. There are two types of triangular matrices: upper triangular and lower triangular.

• An upper triangular matrix has all its non-zero elements located on or above the main diagonal, while all elements below the main diagonal are zero.
• A lower triangular matrix has all its non-zero elements located on or below the main diagonal, while all elements above the main diagonal are zero.

Triangular matrices have many properties that make them useful in various mathematical computations. For example, they can simplify the process of solving systems of linear equations and computing determinants. Additionally, triangular matrices have efficient algorithms for matrix multiplication and matrix inversion.

Overall, triangular matrices play an important role in linear algebra and find applications in various fields such as engineering, physics, and computer science.