QR decomposition

QR decomposition factors A = QR

QR decomposition is a fundamental concept in linear algebra that breaks down a matrix into simpler components. It involves expressing a matrix A as the product of an orthonormal matrix Q and an upper triangular matrix R. This decomposition is crucial for solving linear least squares problems and is the foundation for the QR algorithm used in eigenvalue computations.

Example

Consider a matrix A = [1, 2; 3, 4]. The QR decomposition of A results in Q = [0.3162, -0.9487; 0.9487, 0.3162] and R = [3.1623, 4.4272; 0, 1.4142]. Thus, A = QR.

Remember this

Understanding QR decomposition is essential for efficiently solving linear systems and performing eigenvalue analysis in numerical linear algebra.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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