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Numerical algorithms for problems in analysis and algebra, scientific computation

2 votes
1 answer
276 views

Possible pathological properties of positive definite matrix

Suppose $A$ is a positive definite matrix such that$$ I \preceq A \preceq 1.01I.$$ Is it possible that $\sum\limits_{i=1}^n A_{1i}$ can be arbitrarily large?
Jack Lee's user avatar
1 vote
0 answers
374 views

The rationale of QR algorithm for computing eigenvectors

For a symmetric matrix $A$, the rationale for the success of applying QR to compute the spectral decomposition of $A = UDU^T$ is, for large $k$, the QR factorization of $A^k = Q_kR_k$ obeys, \begin{eq …
Jack Lee's user avatar