Conjugate transpose

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Explains matrix operations, orthogonality, and least squares method in solving linear equations.

Covers the properties of orthogonal matrices and their eigenvalues.

Explores the properties and applications of matrix transpose, including rotations and inverse matrices.

Explains ray vectors, matrices, and properties of paraxial optical systems, with examples of conjugate matrices for thin lens imaging systems.

Analyzes plasma instabilities through case studies, exploring the implications of roots in the complex plane.

Covers Cramer's Rule for solving linear equations and calculating matrix inverses.

Explores envelope representations, subgradients, and the duality gap in convex optimization.

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

Explores envelope representations, subgradients, conjugate functions, duality gap, and strong duality in convex optimization.

Covers the representation of complex numbers and their applications in mathematical transformations.