I'm currently taking a numerical analysis course. We are covering linear algebra topics, the gist of the first chapter of the course being solving systems of linear equations. The lecturer has introduced SVD decomposition, condition number of a matrix, LU decomposition and QR decomposition (using Householder decomposition).
In the past I've been used to very rigorous, thorough and well-organized math courses. But I feel like what I'm learning here is shallow since there are very few proofs.
So my question is
Can you recommend rigorous textbooks or detailed lecture notes that cover the topics I mentioned above ?
Best Answer
The following books cover all the topics that you mention rigorously. They are required reading in the field of numerical analysis and require a solid background in pure mathematics.
Higham, N. J: "Accuracy and stability of numerical algorithms", SIAM, (2002)
Golub, G. H and van Loan, C. : "Matrix computations", 4th edition. John Hopkins University Press, (2013)