Linear Algebra: Orthogonal Projection and QR Factorization

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QR Factorization: Least Squares System Resolution

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

Gram-Schmidt Algorithm: Orthogonalization and QR Factorization

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

Singular Value Decomposition: Applications and Interpretation

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

Factorisation QR: Gram-Schmidt Process

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

Untitled

Singular Value Decomposition: Fundamentals

Covers the fundamentals of Singular Value Decomposition, including properties, applications, and error measurement.

Least Squares Solutions

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

QR Factorization and Least Squares

Explores QR factorization and the least squares method for solving systems of equations.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.