Decomposition of Linear Operators

Related lectures (30)

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Explores the matrix representation of operators and basis transformation in linear algebra.

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Covers the reduction of a linear transformation in a 2-dimensional space to find a simpler matrix representation.

Covers eigenvalues and eigenvectors, explaining their importance in linear algebra.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Covers the theory and applications of orthogonal projections, focusing on the Gram-Schmidt process for orthonormalization.

Covers the process of determining if a matrix is diagonalizable.

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.