Learn · Matrix Analysis with Applications
Lecture 2 of 40Week 1
Echelon form of a matrix
Prof. S. K. Gupta and Prof. Sanjeev Kumar · IIT Roorkee
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- Matrix Analysis with Applications, IIT Roorkee (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Elementary row operations
- Echelon form of a matrix
- Rank of a matrix
- System of Linear Equations-I
- System of Linear Equations-II
- Introduction to Vector Spaces
- Subspaces
- Basis and Dimension
- Linear Transformations
- Rank and Nullity
- Inverse of a Linear Transformation
- Matrix Associated with a LT
- Eigenvalues and Eigenvectors
- Cayley-Hamilton Theorem and Minimal Polynomial
- Diagonalization
- Special Matrices
- More on Special Matrices and Gerschgorin Theorem
- Inner Product Spaces
- Vector and Matrix Norms
- Gram Schmidt Process
- Normal Matrices
- Positive Definite Matrices
- Positive Definite and Quadratic Forms
- Gram Matrix and Minimization of Quadratic Forms
- Generalized Eigenvectors and Jordan Canonical Form
- Evaluation of Matrix Functions
- Least Square Approximation
- Singular Value Decomposition
- Pseudo-Inverse and SVD
- Introduction to Ill-Conditioned Systems
- Regularization of Ill-Conditioned Systems
- Linear Systems : Iterative Methods I
- Linear Systems : Iterative Methods II
- Non-Stationary Iterative Methods: Steepest Descent-I
- Non-Stationary Iterative Methods: Steepest Descent-II
- Krylov Subspace Iterative Methods (Conjugate Gradient Method)
- Krylov Subspace Iterative Methods (CG and Pre-Conditioning)
- Introduction to Positive Matrices
- Non-Negativity and Irreducible Matrices
- Polar Decomposition