Eisenstein Series: Decomposition and Unitarizability

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Covers the QR factorization of a matrix A into Q and R.

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

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

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Explores orthogonal projections, orthonormal bases, and QR factorization in linear algebra.

Explores QR factorization, orthogonal bases, and matrices for numerical computations and solving systems of equations.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Explores orthogonal projections and the Gram-Schmidt method for constructing bases.

Explores spectral and singular value decompositions of matrices.