Course Material for EE2100: Matrix Theory (Fall 2023)

Notes and Scribble

The Scribble and the Notes are intended for quick reference\review. Notes and Scribble are by no means a complete source and infact are based on the suggested textbooks\references. It is highly recommended that the students also refer to the suggested textbooks\references.

Lec. (Date)	Topics Covered	Logistics
1 (31/07)	Introduction [ Scribble ] Course overview Applications of Matrices
2 (02/08)	Vectors and Elementary Operations on Vectors [ Scribble \| Notes ] Vectors and their properties Elementary operations on Vectors: Vector Addition, Scalar Multiplication Dot Product
3 (03/08)	Norm and Cauchy-Schwarz inequality [ Scribble \| Notes ] Geometrical Interpretation of a Vector and Dot Product Norm and its Geometrical Interpretation Cauchy-Schwarz Inequality
4 (07/08)	Projection [ Scribble \| Notes ] Angle between vectors Projection
5 (09/08)	Vector Space [ Scribble \| Notes ] Binary Operation and Field Vector Space
6 (10/08)	Subspace and Span [ Scribble \| Notes ] Few identities of Vector Space Supspace of a Vector Space Linear combination and Span	HW01 out (11/08)
7 (14/08)	Linear Independence, Spanning Set and Basis [ Scribble \| Notes ] Span as a subspace Linear independence Spanning set and Basis
8 (16/08)	Dimension of a Subspace [ Scribble \| Notes ] Dimension of a Subspace Theorems related to dimension of a Subspace
9 (17/08)	Orthogonal Basis [ Scribble \| Notes ] Orthogonal Basis Coordinate vector Representation of a vector in Orthogonal Basis	HW02 out (18/08)
10 (21/08)	Generation of Orthogonal Basis [ Scribble \| Notes ] Grahm Schmidt Algorithm Projection of a Vector onto a Subspace	HW01 due (21/08)
11 (23/08)	Projection of a Vector onto a Subspace [ Scribble \| Notes ] Projection of a vector onto a Subspace Introduction to k-Means clustering
12 (24/08)	k-Means clustering [ Scribble ] k-Means clustering Convergence Aspects	HW03 out (25/08)
13 (28/08)	Introduction to Matrices [ Scribble \| Notes ] Introduction to Matrices Elementary Matrix Operations	HW02 due (21/08)
14 (30/08)	Matrix Vector Product [ Scribble \| Notes ] Matrix Vector Product Introduction to Linear Transformation
15 (31/08)	Linear Transformation and Matrices [ Scribble \| Notes ] Linear Transformations and Transformation Matrices Transformation matrices in 2D ( $mathcal{R}^2rightarrowmathcal{R}^2$ )	HW04 out (01/09)
16 (04/09)	Inverse of a Matrix [ Scribble \| Notes ] Matrix Multiplication Elementary Row operations and Matrix Multiplication	HW03 due (04/09)
17 (06/09)	Matrix Multiplication [ Scribble \| Notes ] Matrix Vector Product Introduction to Linear Transformation
18 (07/08)	Fundamental Subspaces [ Scribble \| Notes ] System of Linear Equations Fundamental Subspaces of a Matrix	HW05 out (08/09)
19 (11/09)	Rank-Nullity Theorem [ Scribble \| Notes ] Rank and Nullity of a Matrix Rank-Nullity Theorem
20 (13/09)	Gaussian Elimination [ Scribble \| Notes ] Back-Substitution to solve Forward-Elimination	HW04 due (13/09)
21 (14/09)	Gaussian Elimination [ Scribble \| Notes ] Gaussian Elimination for Characterizing Null Space Inconsistent system of linear equations	HW06 out (15/09)
22 (18/09)	LU Decomposition [ Scribble ] Introduction to LU decomposition Elementary row operations and lower triangular matrices	HW05 due (18/09)
23 (20/09)	LU Decomposition [ Scribble ] Inverse of lower triangular matrices corresponding to elementary row operations LU decomposition and solving system of linear equations
24 (21/09)	Overdetermined System of linear equations [ Scribble \| Notes ] Overdetermined system of linear equations Projection Matrix	HW07 out (22/09)
25 (25/09)	Linear Regression [ Notes ] Overview of Regression Linear Regression	HW06 due (26/09) HW08 out (29/09)
26 (04/10)	Trace and Determinant [ Scribble \| Notes ] Trace of a Matrix Introduction to Determinant of a Matrix	HW07 due (03/10)
27 (05/10)	Determinant of a Matrix [ Notes ] Determinant of a Matrix Computation of Determinant	HW09 out (06/10)
28 (09/10)	Eigen Values and Eigen Vectors [ Notes ] Introduction to Eigen Values and Eigen Vectors
29 (11/10)	Eigen Values and Eigen Vectors [ Notes ] Eigen Values and Eigen Vectors of Real and Symmetric Matrices LU decomposition and solving system of linear equations
30 (12/10)	Spectral Theorem [ Notes ] Quadratic Forms Rayleigh Quotient	HW10 out (15/10)
31 (16/10)	Positive Definite Matrices [ Scribble \| Notes ] Quadratic Forms Positive and Negative definite/semidefinite matrices	HW08 due (16/10)
32 (18/10)	QR Decomposition [ Scribble \| Notes ] Grahm Schmidt and QR Decomposition Householder Transformation
33 (19/10)	Cholesky Decomposition [ Scribble ] Decomposition of Positive semidefinite Matrices Cholesky Decomposition	HW11 out (20/10) HW09 due (23/10)
34 (30/10)	Decompositions and Solving Systems of Linear Equations Cholesky Decomposition and Solving System of Linear Equations Dolittle Method for LU Decomposition
35 (01/11)	Singular Value Decomposition [ Scribble \| Notes ] Introduction to Singular Value Decomposition Singular Values and Singular Vectors
36 (02/11)	Norm of a Matrix [ Scribble \| Notes ] Representation of Matrix as a Sum of Rank-1 Matrices Norm of a matrix	HWs 10&11 due (03/11) HW12 out (04/11)
37 (06/11)	Condition Number of a Matrix [ Scribble \| Notes ] Significance of Condition Number Condition Number of a Matrix
38 (08/11)	Principal Component Analysis Need for dimensionality reduction Mean and Variance of Data sets.
39 (09/11)	Principal Component Analysis Role of Singular Values in Principal Component Analysis Algorithm for dimensionality reduction	HW13 out (10/11) HW 12 due (14/11)
40 (15/11)	Jordan Forms [ Scribble ] Defective Matrices Generalized Eigen Values Jordan Forms
41 (20/11)	Similar Matrices [ Scribble ] Notion of Similarity between Matrices. Properties of Similar Matrices.	HW14 out (19/10) HW 13 due (20/11)
		HW14 due (29/11)