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Linear Algebra (MATH106)

Systems of linear equations: elementary row operations, echelon forms, Gaussian elimination method. Matrices: elementary matrices, invertible matrices, symmetric matrices, quadratic forms and Law of Inertia. Determinants: adjoint and inverse matrices, Cramer's rule. Vector spaces: linear independence, basis and dimensions, Euclidean spaces. Linear mappings: matrix representations, changes of bases. Inner product spaces: Cauchy-Schwarz inequality, Gram-Schmidt orthogonalization. Eigenvalues and eigenvectors: characteristic polynomials, Cayley-Hamilton Theorem, Diagonalization, basic ideas of Jordan forms.

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