Concept

Kernel (set theory)

Related lectures (8)

Linear Transformations: Dimension Theorems

Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Groups and Homomorphisms

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Linear Applications: Kernel-Image Theorem

Explores the Kernel-Image Theorem, bijectivity conditions, linear forms, and surjectivity in linear algebra.

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Neural Network: Random Features and Kernel Regression

Covers random features in neural networks and kernel regression equivalence.

Canonical Correlation Analysis: Linear and Kernel CCA

Introduces Canonical Correlation Analysis for finding joint features in separate datasets, extending to multimodal data and non-linear features.

Kernels: Nonlinear Transformations

Explores kernels for simplifying data representation and making it linearly separable in feature spaces, including popular functions and practical exercises.