Maha Hassanein

0

Review: Basics of Linear Algebra; Vector Space, Subspace, Basis, Linear Transformations and matrices, Ranges, Null spaces, .. ,

Elementary matrix operations  and systems of linear equations

[REF2].  Chapter 1,2,3,6.1

[REF1] Lecture 1 :Matrix vector multiplication

Lecture 2 :Orthogonal vectors and matrices

1

Review: Inner product Space basic properties; norms, unitary transformations)

                 Vector and Matrix norms

Classical Gram-Schmidt (CGS) Orthogonalization

[REF1].  Lecture 3: Norms

[REF2] Sec 6.1 : Inner Products and norms

Sec. 6.2 : Gram-Schmidt Orthogonaliztion

2

Singular Value Decomposition (SVD)

Properties and Applications of SVD

 [REF2] Sec 6.7

 [REF1].  Lecture 4-5

3

Dual Space. Review : Adjoint operator

Unitary and orthogonal operators

Orthogonal Projection

Spectral Theorem for normal matrices

Bilinear forms and Quadratic forms

Pseudo inverse

[REF2] Sec 2.6:Dual Space ;

[REF2] Sec 6.5 : Unitary and

orthogonal operators

Sec 6.6 : Orthogonal Projection and the spectral theorem ;

Sec 6.7 : Pseudo inverse

Sec.6.8: Bilinear and quadratic forms

[REF1] Lecture 6: Projectors

4

QR factorization

Classical Gram-Schmidt (CGS) Orthogonalization (revisited)

Modified Gram-Schmidt (MGS)

[REF1] 

Lecture 7: QR-factorization

Lecture 8: Gram-Schmidt

5

Householder Triangularization

[REF1].  Lectures 10

6

Least squares problem and pseudoinverses

[REF1]  Lecture 11

7

Gaussian Elimination

Conditioning and Stability

[REF1].  Lectures 12,20,21,23

[REF2] Sec 6.9 : Conditioning and the Rayleigh Quotient

8

Eigenvalue problem:

EigenSpace, Diagonalization,           

[REF1].  Lectures 24,25

9

Schur Decomposition for Triangularization

Gershgorin Theorem

10

Positive Definite Matrices        

11

Discussions

12

Discussions

13

REVISION