## New answers tagged matrix-analysis

1
vote

### Questions on symmetric Hadamard matrices

Currently, this is an open problem. So I only got a partial answer.
We just need to consider the following two different situations:
Case 1: $n$ is not a perfect square. There is no solution if $\...

5
votes

Accepted

### Forming real positive semidefinite matrices from complex matrices

We say that a matrix $O$ is complex orthogonal if $O^TO=I$ where $I$ denotes the identity function. If $n>1$, then there are many complex orthogonal matrices that are not real orthogonal matrices.
...

4
votes

### Unitary transformations of Vandermonde matrices forms a smooth manifold?

The answer is 'not always', in particular, not when $(n,r)=(2,3)$.
The image is obviously is a smooth manifold when $n=0$, for then the image in $\mathbb{R}^{(n+1)r}=\mathbb{R}^r$ is the sphere $\...

0
votes

### Generate a low-rank sparse covariance matrix

Matlab's sprandsym generates a random sparse positive-definite matrix by starting from a diagonal matrix and applying to it Jacobi rotations, i.e., rotation ...

2
votes

Accepted

### Where does $V$ from the spectral decomposition $A = VDV^*$ lie, if $A$ has only imaginary entries?

The $n\times n$ imaginary matrix $A$ satisfies $A^\top=-A$, so it is skew-symmetric. The Youla decomposition is
$$A=iO\Sigma O^\top,$$
where $O$ is a real orthogonal matrix and $\Sigma$ is a real ...

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