NPTEL Awareness workshop in association with Gandhinagar Institute of Technology, Gandhi Ngr Gujarat

Please fill this Feedback form to obtain the participation e-certificate - https://ift.tt/35OcqDl NPTEL Awareness workshop in association with Gandhinagar Institute Of Technology, Gandhi Nagar, Gujarat

Courant-Fischer theorem

Courant-Fischer theorem Statement and proof of the Courant Fischer Theorem

Variational characterization of eigenvalues (continued)

Variational characterization of eigenvalues (continued) Further results on variational characterization of eigen values

Variational characterization of Eigenvalues: Rayleigh-Ritz theorem

Variational characterization of Eigenvalues: Rayleigh-Ritz theorem Properties of Hermitian Matrices, Spectral Theorem for hermitian matrices, Rayleigh - Ritz Theorem

Properties of hermitian matrices

Properties of hermitian matrices Properties of Hermitian Matrices, Spectral Theorem for hermitian matrices, Rayleigh - Ritz Theorem

Hermitian and symmetric matrix

Hermitian and symmetric matrix Hermitian and symmetric matrix

Cholesky decomposition and uses

Cholesky decomposition and uses Definition of positive definite matrix, Cholesky decomposition and uses, Review of Jordan canonical form and how to find JCF

Solving pivoted system and LDM decomposition

Solving pivoted system and LDM decomposition Solving pivoted systems, Pivoting when A is rank deficient, LDM and LDL^T decomposition

LU decomposition with pivoting

LU decomposition with pivoting Permutation Matrices, LU decomposition with pivoting

LU decomposition

LU decomposition LU Decomposition, Gauss Transforms, Permutation Matrices

Other canonical forms and factorization of matrices: Gaussian elimination & LU factorization

Other canonical forms and factorization of matrices: Gaussian elimination & LU factorization

Polynomials and matrices

Polynomials and matrices Monic Polynomial, Minimal polynomial

Properties of convergent matrices

Properties of convergent matrices Convergence of non diagonalizable matrices

Properties of the Jordan canonical form (part 2)

Properties of the Jordan canonical form (part 2) Part 2. Polynomial construction with Jordan form, Property of upper triangular Toeplietz form

Properties of the Jordan canonical form (part 1)

Properties of the Jordan canonical form (part 1) Part 1. Non-derogatory matrix, Polynomial expansion of a matrix, Upper triangular Toeplitz form

Determining the Jordan form of a matrix

Determining the Jordan form of a matrix how to get Jordan canonical form of a matrix, uses of Jordan Canonical form

Jordan canonical form

Jordan canonical form Jordan form theorem

QR decomposition and canonical forms

QR decomposition and canonical forms (a) QR Decomposition (b) QR Algorithm (c) Canonical Form (d) Introduction to Jordan Canonical Form

Fundamental properties of normal matrices

Fundamental properties of normal matrices (a) Fundamental properties of Normal Matrix- Theorem and Proof (b) Spectral theorem for Hermitian Matrix

Normal matrices: Definition and fundamental properties

Normal matrices: Definition and fundamental properties The definition and fundamental properties of normal matrices

Uses of cayley-hamilton theorem and diagonalizability revisited

Uses of cayley-hamilton theorem and diagonalizability revisited Uses of Cayley-Hamilton Theorem: Expressing higher power of a matrix as a linear combinations of the lower powers of that matrix Finding inverse of non-singular matrices using Cayley-Hamilton theorem Diagonalizability Revisited How to find an arbitraily close diagonalizable matrix to a given matrix Theorems relatied to similar matrices given any arbitray matrix

Who's in line for the British throne?

Learn who's next in line to inherit the royal throne and where Harry and Meghan's youngest child, Lilibet Diana Mountbatten-Windsor, falls in the lineup.

Who's in line for the British throne?

Learn who's next in line to inherit the royal throne and where Harry and Meghan's youngest child, Lilibet Diana Mountbatten-Windsor, falls in the lineup.

NPTEL Awareness workshop in association with Parala Maharaja Engineering College, Berhampur, Odisha

Please fill this feedback form to obtain an e-participation certificate : https://ift.tt/3waOwOe NPTEL Awareness workshop in association with Parala Maharaja Engineering College, Berhampur, Odisha

Cayley-Hamilton theorem

Cayley-Hamilton theorem (a). Cayley-Hamilton Theorem and proof

Recap of matrix norms and Levy-Desplanques theorem

Recap of matrix norms and Levy-Desplanques theorem Spectral norm and radius, norm of inverse of a matrix, invertability of diagonally dominant matrix

Convergent matrices, Banach lemma

Convergent matrices, Banach lemma Properties of spectral radius, convergent matrices and associated lemmas, Banach lemma

Cayley-Hamilton Theorem

Cayley-Hamilton Theorem Cayley-Hamilton Theorem and proof

Schur's Triangularization Theorem

Schur's Triangularization Theorem (a). Recap of unitary equivalence. (b). Schur's Triangularization theorem for complex matrices and proof. (c). Schur's Triangularization theorem for real matrices. (d). Properties

Unitary Equivalence

Unitary Equivalence Unitary Equivalence, Euclidean Isometry

Properties of Unitary Matrices

Properties of Unitary Matrices Properties of unitary matrices

Unitary Matrices

Unitary Matrices Unitary Matrices, Proof for orthogonal vectors being linearly independent

Eigenvector and principle of biorthogonality

Eigenvector and principle of biorthogonality

Relationship between eigenvalues of BA and AB

Relationship between eigenvalues of BA and AB

Diagonalization

Diagonalization Similarity transform and diagonalization

Similarity

Similarity Distinct eigen values and linear independence of eigen vectors,

Solving characteristic polynomials, eigenvectors properties

Solving characteristic polynomials, eigenvectors properties Procedure to solve characteristic polynomials, eigenvectors properties

The Characteristic Polynomial

The Characteristic Polynomial Characteristic polynomials

Introduction to Eigenvalues and Eigenvectors

Introduction to Eigenvalues and Eigenvectors Definition of eigenvalues and eigenvectors, procedure to find eigenvalues and eigenvectors

Errors in solving systems of linear equations

Errors in solving systems of linear equations Bounding the accuracy and finding relative errors of solutions to system of linear equations, proof for compatability between vector and Matrix norms

Errors in inverses of matrices

Errors in inverses of matrices Errors in inverses of Matrices, some properties of condition number

Equivalence of matrix norms and error in inverses of linear systems

Equivalence of matrix norms and error in inverses of linear systems Unitarily invariant norms, Self-adjoint norms, Erros in calculating inverse of a matrix due to perturbation of entries

Recap of matrix norms and levy-desplanques theorem

Recap of matrix norms and levy-desplanques theorem Bounds on the norm of the inverse of a matrix, Banach lemma, Levy-Desplanques theorem

Convergent matrices, banach lemma

Convergent matrices, banach lemma Properties of spectral radius, convergent matrices and associated lemmas, Banach lemma

Properties of Spectral Radius

Properties of Spectral Radius Proof of lemma introduced at the end of Spectral radius

Spectral radius

Spectral radius

Induced norms and examples

Induced norms and examples