Canonical Transformations: Symplectic Group and Properties

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Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Covers matrix multiplication, properties, and inverses in linear algebra.

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Covers the fundamentals of linear equations, matrices, and systems of linear equations, including matrix operations and solutions.

Covers the definition and basic operations of matrices, including addition, scalar multiplication, and matrix multiplication.

Covers matrix invertibility, determining if a matrix is invertible, calculating its inverse, and elementary matrices.

Covers matrix addition, scalar multiplication, transposition, symmetry, and antisymmetry properties.