Video Lectures
Matrices in Special Forms
Diagonal Matrices
Upper and Lower Triangular Matrices
Permutation matrices
Elementary matrices
Their conceptual idea
Constructing them using the identity matrix
Finding their inverses
LU decomposition
Algorithm
Examples
LDU and PLU decompositions
Algorithm of constructing Permutation Lower-Upper Triangular (PLU) decomposition
The conceptual idea of PLU decomposition
Algorithm of constructing Lower-Diagonal-Upper Triangular (LDU) decomposition
LU decomposition to solve Systems of Linear Equations
Construct the A = LU decomposition
Split the system Ax = b into two systems Ly = b and Ux = y
Solve the two systems (Ly=b, Ux = y) by performing one time forward and one time backward substitution
Quizzes and Assignments