Matrix Transformation: Canonical Basis

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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

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

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Explores linear transformations, matrices, injective and surjective functions, and their applications.

Covers the composition and product of matrices, including matrix multiplication.

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Explores the motivation behind change of basis in linear algebra, emphasizing the importance of selecting the right basis.

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

Explores density operator matrix transformation in quantum physics and the implications of measuring the system, leading to state collapse.