Video Lectures
Applied mathematics has two parts
1. Find the equation
2. Solve the equation
When we find the equation we then get a matrix
Properties of
Symmetric matrix (i.e. K = K Transpose)
Has an inverse can't say by just glancing it i.e. Non-Singular
Tri-Diagonal (only main diagonal and one each above and below)
Constant Diagonal (same numbers on diagonal). We can do a lot with Fourier Analysis on these kind of matrices
Positive Definite Matrix - has n pivots and all n positive pivots
All n EigenValues are Positive
(Any Vector X) * Matrix * (Transpose of Vector X) is also positive
How to tell if matrix is invertible?
Solutions
1. Check itz Determinant. Determinant is not zero for invertible matrix
2. B.x=0 i.e there is a matrix x not equal zero that takes B to Zero
3. Pivots are never zero
Solve equations by
Matrix = Lower Triangular * Symmetric Diagonal * Transpose of Lower Triangular
Four Pillars of Linear Algebra
1. Elimination
2. Grams-Schmidt
3. Eigenvalue
4. Fourier Analysis
