Elementary symmetric polynomial

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Explores properties of operations, equivalence relations, and logic basics.

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Explores real functions, covering parity, periodicity, and polynomial functions.

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.

Explores general conics, motor blocks, and homo coordinates in matrix decomposition and coefficient calculations.

Explores subspaces, approximation problems, and least-squares approximation methods.

Explores unconstrained optimization theory, covering global and local minima, convexity, and gradient concepts.

Covers linear approximations up to order 2 and the Hessian matrix.

Explores Gaussian corelation inequality, Anderson's theorem, and log-concavity in probability theory.

Explores orthogonal diagonalization of symmetric matrices using orthonormal bases and the Gram-Schmidt method.