Lectures related to Principal Series Representations in Mathematics

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Explains methods for finding eigenvalues in linear algebra through examples.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Covers the organization of linear algebra course and exercises for civil engineering and environmental sciences students.

Explores matrices, change of bases, eigenvectors, eigenvalues, and vector spaces.

Covers the reduction of non-diagonalizable matrices and their geometric interpretations.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Covers the reduction of matrices, eigenvalues, eigenvectors, and geometric interpretations in vector spaces.

Covers electronic structure calculations using quantum mechanics and introduces fundamental concepts in computational quantum chemistry.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

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