Hermitian Spaces: Theory and Applications

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Related lectures (31)

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Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Scalar Product and Euclidean Spaces

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Iterative Methods for Linear Equations

Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.

Linear Quadratic (LQ) Optimal Control: Proof of Theorem

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.

Iterative Methods for Linear Equations

Explores iterative methods for linear equations, including Jacobi and Gauss-Seidel methods, convergence criteria, and the conjugate gradient method.