Permutations and Adjacency

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Related lectures (28)

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Dihedral Group: Symmetries and Cosets

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Linear Applications and Span

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Lorentz Transformations and Covariant Tensors

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Matrix Dimension Calculation

Explains how to calculate the dimension of a kernel of a matrix transpose.

Linear Algebra: Change of Basis and Matrix Representation

Explores changing bases in vector spaces and matrix representation of linear transformations.

Linear Transformations: Isomorphism and Dimension

Covers isomorphism, dimension, bases, and rank in linear transformations between vector spaces.

Linear Transformations: Matrices and Bases

Covers the method to calculate the images of vectors in a given base.

Linear Transformation Properties

Explores the properties of linear transformations through step-by-step calculations and matrix manipulations.

Endomorphisms: Matrix Equivalence

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.