Bruhat decomposition

Bruhat Decomposition is a way of looking at matrices and how they can be changed. It is a way of "breaking down" a matrix into simpler parts to understand it better. A matrix is a collection of numbers arranged in rows and columns, like a grid.

Bruhat Decomposition says that a matrix can be separated into two matrices that are both smaller and simpler than the original matrix. These two matrices are called Upper Triangular Matrix and Lower Triangular Matrix. The Upper Triangular Matrix has all the numbers in the upper half of the grid, and the Lower Triangular Matrix has all the numbers in the lower half of the grid.

Together, these two matrices contain all of the same information as the original matrix, but in different forms. It can be helpful to look at the Upper and Lower Triangular Matrices because it can be easier to understand what the original matrix is doing and how it can be changed.