Matrix Factorization: Least Squares Method

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Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Covers least squares solutions for linear systems using matrix operations and normal systems, illustrated with examples.

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explores the properties of invertible matrices, including unique solutions and linear independence.

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.