Matrix Decomposition: QR Factorization

This lecture covers the QR factorization method for decomposing a matrix A into the product of an orthogonal matrix Q and an upper triangular matrix R. The instructor explains the process step by step, highlighting the importance of this decomposition in various applications. The lecture also discusses the conditions for the matrix A to be invertible and the implications of a well-chosen model. Through examples and proofs, the lecture demonstrates the significance of QR factorization in solving systems of linear equations and its role in numerical stability. The lecture concludes with a detailed explanation of the Gram-Schmidt orthogonalization process and its application in matrix decomposition.