Orthogonality and Least Squares Method

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Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

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

Covers the application of systems of linear differential equations of the first order.

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

Covers methods to solve linear differential equations in systems with initial conditions.

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Explores linear combinations, matrix-vector product, and matrix equation solutions.