Lectures related to Linear Applications: Definitions and Examples

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Linear Algebra: Change of Basis Matrices

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Galilean Transformations: Spacetime and Measurements

Explores Galilean transformations in spacetime, focusing on measurements and coordinate transformations.

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Properties of Fourier Transform

Explores the properties and applications of the Fourier transform in signal processing and mathematics.

Isometries: Definition and Examples

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Eigenvalues and Eigenvectors: General Definition and Examples

Explores eigenvalues, eigenvectors, and diagonalizable transformations through various examples.

Lorentz Transformations and Covariant Tensors

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

Linear Algebra: Matrices and Vector Spaces

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

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Linear Transformations and Change of Bases

Covers linear transformations, change of bases, and diagonalization of matrices.

Critical Behavior in General Relativity

Explores critical behavior in general relativity, including scaling factor and coupling constant flow.

Coordinate Systems and Applications

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Linear Applications: Properties and Associated Matrices

Explores linear applications, matrix-vector products, and the linearity of transformations.

Linear Applications and Matrices

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.