Lectures related to Frobenius inner product

Exponential of a Matrix

Explores the exponential of a matrix, properties, Frobenius norm, nilpotent matrices, commutativity, and system solutions.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Orthogonality and Projections

Demonstrates computing inner products and projections between vectors in a given space.

Advanced analysis II: local inversion theorem

Covers the local inversion theorem and uniqueness of solutions in a ball around a point.

Quantum Physics I

Covers state vectors, Dirac notation, inner product, eigenvectors, and operators in quantum physics.

Orthogonal Matrices, Equivalences

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Radial Quantization & Inner Products

Covers radial quantization and inner products in quantum field theory.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, focusing on states, time evolution, and measurement.

Quaternion Algebra and Hermite Space

Covers quaternion algebra, Waldspurger formula, and Hermite space in relation to L-functions and inner products.

Conformal Field Theory: Generators and Commutation Relations

Covers the definition of generators of the conformal group and the application of Wick's theorem.

The space of bandlimited functions

Explores the space of bandlimited functions, focusing on 1-bandlimited functions as a basis and their representation through sequences.

Matricizations and Alternating Least Squares

Covers matricizations, ALS method, and tensor decomposition, emphasizing the alignment of fibers in matrices.

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Quantum Physics I

Covers state vectors, Dirac notation, eigen-kets, and Hermitian operators in quantum physics.

Singular Value Decomposition: Theory and Applications

Explores Singular Value Decomposition theory, properties, uniqueness, matrix approximation, and dimensionality reduction applications.

Linear Algebra in Dirac Notation

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Orthogonal Bases, Orthonormal/Orthonormalized Bases

Introduces orthogonal and orthonormal families in vector spaces with scalar products.

Signal spaces: Inner product, infinite-length signals, and completeness

Covers signal spaces, inner product, infinite-length signals, and completeness in vector spaces.