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

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.

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

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

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Covers the factorization of a matrix and the least squares method.

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the Factorisation QR theorem and the Gram-Schmidt method for orthonormal bases.

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

Explains row-echelon and reduced row-echelon matrices and their role in simplifying system resolution.

Covers the concept of the matrix of cofactors and a formula to calculate the inverse of a matrix.

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

Explains how to solve linear equations using the least squares method to minimize errors in the system.

Covers linear applications, matrices, transformations, and the principle of superposition.