References for Vector space: 1) Analysis in Vector space: Ackoglu, Bartha & Ha (Short loan) 2) Survey of Modern Algebra: Birkhoff, MacLane 3) Lectures on Linear Algebra: I. M. Gelfand 4) Abstract Linear Algebra: Morton L. Curtis (Short loan) 5) Linear Algebra, An introductory approach: Charles W. Curtis (Short loan) 6) Linear Algebra (UTM): Serge Lang 7) Finite-Dimensional Vector Spaces: Paul R. Halmos 8) You will find what you want in most books on Abstract Algebra, for eg: books by Michael Artin, Hoffman & Kunze, Herstein etc.
Lecture 17: Four fundamental subspaces for a matrix
12 September - 18 September
Lecture 18: Four fundamental subspaces for a matrix
Lecture 19: Four fundamental subspaces of a matrix
Lecture 20: Direct sum, Orthogonal subspaces.
19 September - 25 September
Lecture 21: Least Square solution to Ax = b
Lecture 22: Least square solution to Ax = b, Projection to Range(A)
Lecture 23: Gram-Schmidt Orthogonalization
26 September - 2 October
Lecture 24: QR Factorization, Fourier transforms, Field of Complex numbers
Reference on Completion of Normed Vector Spaces & Lp spaces: The Lebesgue Stieltjes Integral- A Practical Introduction, M. Carter & B. van Brunt. e-book in Lecture/Aditya Tatu/CT501/ Refer pages: 24-25: Definition of Step functions 39-40: Definition of Riemann Integral 46-48: Dirichlet function 135-138: Completion of spaces (general) 138-150: L1,Lp spaces
For those interested in understanding Lebesgue Integral, refer Chapter 4