Lectures related to QR decomposition

QR Factorization: Least Squares System Resolution

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

Integration of Simple Elements

Covers the integration of simple elements and limit expansions with examples.

Orthogonal Projections and Reflections

Covers the analytical expression of orthogonal projections and reflections in 2D space.

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Matrix Calculus: Rank and Decomposition

Covers matrix rank, determinant, and decomposition in linear algebra.

SVD: Singular Value Decomposition

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

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Bipartite systems - Entanglement

Covers the concept of entanglement in bipartite systems, focusing on entropy and Schmidt decomposition.

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

MIMO Receivers

Covers the system model, linear receivers, performance evaluation, and graphical interpretations of MIMO receivers, including maximum likelihood detection and successive interference cancellation.

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Architectural Transformations: Design Space Exploration

Explores architectural transformations optimizing area, time, and product in digital system design.

Least Squares Solutions

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

Laplace Equation: Decomposition and Solutions

Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.

Vector Spaces: Structure and Bases

Covers vector spaces, bases, and decomposition of vectors in R³.

Singular Value Decomposition: Image Compression and Applications

Covers Singular Value Decomposition, focusing on its application in image compression and data representation.

Gram-Schmidt Algorithm: Orthogonalization and QR Factorization

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

Orthogonal Bases and Projection

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Direct Methods for Linear Systems of Equations

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.