Lecture

Matrix Calculus: Rank and Decomposition

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Description

This lecture covers the concepts of matrix rank, determinant, and decomposition, illustrating how to calculate them and their implications in linear algebra. The instructor explains the relationships between rows and columns, the number of pivots, and the properties of matrices. Various examples are provided to demonstrate the application of these concepts.

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

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Planetary boundary layer

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QR decomposition

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).

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