Wiwat Wanicharpichat

4 Questions 132 Answers 0 Followers

Questions related from Wiwat Wanicharpichat

How to verify that AA^{∗} + BB^{∗} and A^{∗}A + B^{∗}B are positive definite where A is non-singular?

Due to R. Penrose. Any matrix can be partitioned in the form [A BC CA⁻¹B] (using a suitable arrangement of rows and columns), A being any non-singular submatrix whose rank is equal...

30 July 2016 4,732 10 View

What is the Moore-Penrose inverse, or the group inverse of a product matrices which one matrix is invertible and another one is noninvertible?

Let A, B ∈ ℂn×n where A is an invertible matrix (and A⁻¹ ≠ AT), but B is a noninvertible. Let C = AB. What is C†? (C† is the Moore-Penrose inverse of C). Suppose that rank C = rank C². What is C#?...

24 July 2016 1,901 19 View

Is any arrowhead matrix similar to a tridiagonal matrix?

There are some algorithms for transforming arrowhead matrices to tridiagonal form. Is any arrowhead matrix similar to a tridiagonal matrix? What techniques can we use to prove that an arrowhead...

18 January 2016 2,293 9 View

How can we relate flip-eigenvector with (generalized) eigenvalue problem?

Suppose Ax = λx, where x ≠ 0. Let P be a permutation matrix, if we premultiplying above equation by P, PAx = λPx =: λy, say, effect flip arrays (reverses the order of the elements) in the vertical...

13 March 2015 1,421 20 View