What is the concept of QR decomposition in Numerical Analysis?

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What is the concept of QR decomposition in Numerical Analysis?

QR decomposition, also known as QR factorization, is a numerical technique used in numerical analysis to decompose a matrix into the product of two matrices: an orthogonal matrix (Q) and an upper triangular matrix (R). The QR decomposition is widely used in various numerical algorithms, such as solving linear systems of equations, least squares problems, and eigenvalue computations. It provides a convenient way to analyze and manipulate matrices, allowing for more efficient and accurate numerical computations.