Matrix Calculations: Basis Change and Extensions

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Related lectures (24)

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Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Complex Numbers: Applications and Representations

Explores the origin, applications, and representations of complex numbers in crystallography and materials science, including their graphical, polar, and exponential forms.

Vector Spaces in R2 and R3

Covers vector spaces in R2 and R3, including examples of proportional families and coordinate transformations.

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Combinations and Basis Characterization

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Linear Transformations and Basis Changes

Covers the concept of interesting subspaces related to matrices and the change of basis matrix.

Linear Algebra: Vector Spaces

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Vector Subspaces in R4

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.