Lectures related to Mercer Theorem and Kernels

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Vector Spaces: Properties and Operations

Explores vector space properties, operations, linear combinations, and subspaces construction.

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Unitary Representations: Schur's Lemma

Explains Schur's Lemma on unitary representations and their irreducibility and invariance properties.

Diagonalization of Matrices: Eigenvectors and Eigenvalues

Covers the concept of diagonalization of matrices through the study of eigenvectors and eigenvalues.

Support Vector Machines: Kernel SVM

Explores non-linear SVM using kernels for data separation in higher-dimensional spaces, optimizing training with kernels to avoid explicit transformations.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.