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I'm Sujoy from India. Today you'll learn how to find QR Decomposition or QR Factorization of square matrix by Gram Schmidt Orthogonalization with detailed explanation.
This is my first video in the series. In my next video,I'll tell you how to find the QR Decomposition directly on Casio fx-991ES Scientific Calculator !!
Topics explained in this video-
1. Basics of matrix algebra
2. How to find orthonormal columns of square matrix
3. How to find length of a vector manually (modulus of a vector)
4. How to find dot product of two vectors manually
5. How to find projection of a vector on another vector
6. How to convert a 3x3 matrix to orthogonal matrix
7. What is lower triangular matrix and upper triangular matrix - explanation
8. Properties of orthogonal matrix Q
9. How to find upper triangular matrix R
10. A = QR demonstration
11. Properties of QR Factorization with Proof on Casio fx-991ES
A = QR
R = QT.A
Q = A.R^-1
QT = Q^-1
QT.Q = Q.QT = I
QR Decomposition is Matrix version of Gram Schmidt Orthogonalization
That's it for now!
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