Lectures in MOOC Linear Algebra (Part 2)

Diagonalizability Criterion MOOC: Linear Algebra (Part 2)

Covers the criterion for diagonalizability of matrices, focusing on comparing examples and understanding the relationship between algebraic and geometric multiplicities of eigenvalues.

Genetic Problem Diagonalization Application MOOC: Linear Algebra (Part 2)

Covers the application of diagonalization to a genetic problem involving flower color proportions in successive generations.

Algebraic Multiplicity, Geometric Multiplicity MOOC: Linear Algebra (Part 2)

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

Rank Theorem: Linear Applications MOOC: Linear Algebra (Part 2)

Covers the Rank Theorem in linear algebra, discussing dimensions and linear independence of vector spaces.

Diagonalization: Examples MOOC: Linear Algebra (Part 2)

Explores examples of diagonalization in linear algebra, focusing on eigenvalues and eigenvectors.

Matrix Transformation: Canonical Basis MOOC: Linear Algebra (Part 2)

Explores constructing matrix transformations in IR4 using canonical bases and the importance of the equality [T]BB' = [id].

Complex Eigenvalues Appendix MOOC: Linear Algebra (Part 2)

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Geometric Examples MOOC: Linear Algebra (Part 2)

Explores geometric examples related to linear applications in algebra.

Linear Transformations: Matrix Representation MOOC: Linear Algebra (Part 2)

Covers linear transformations, matrix representation, determinants, eigenvalues, and eigenvectors.

Diagonalization: Step by Step MOOC: Linear Algebra (Part 2)

Explains the step-by-step process of diagonalization for linear transformations on finite-dimensional vector spaces.

Change of Basis: Example MOOC: Linear Algebra (Part 2)

Illustrates changing basis in linear algebra through a specific example involving a linear transformation in R4.

Matrix of Cofactors and Inverse Matrix Formula MOOC: Linear Algebra (Part 2)

Covers the concept of the matrix of cofactors and a formula to calculate the inverse of a matrix.

Linear Applications of Vector Spaces MOOC: Linear Algebra (Part 2)

Covers linear applications between vector spaces, exploring their properties and uniqueness based on bases.

Change of Basis, General Case MOOC: Linear Algebra (Part 2)

Explores the relationship between matrices under different bases in linear algebra.

Linear Applications and Matrices MOOC: Linear Algebra (Part 2)

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.

Applications inversibles MOOC: Linear Algebra (Part 2)

Explores invertible linear applications, focusing on bijectivity conditions and orthogonal symmetry transformations.

Eigenvalues: Finding Methods MOOC: Linear Algebra (Part 2)

Explains methods for finding eigenvalues in linear algebra through examples.

Eigenvalues and Eigenvectors: Definitions, Examples MOOC: Linear Algebra (Part 2)

Explains eigenvalues and eigenvectors in linear algebra with practical examples and properties of matrix transformations.

Matrix Transformation Methods MOOC: Linear Algebra (Part 2)

Covers methods for transforming matrices and finding bases for different spaces.

Matrix Operations: Rank and Inclusion in Vector Spaces MOOC: Linear Algebra (Part 2)

Explores matrix rank and vector space inclusion through elementary row operations.