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Results tagged with linear-algebra
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user 490128
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
5
votes
About the Hadamard conjecture
Using the Paley construction I, we obtain Hadamard matrices of size $4, 8, 12, 20, 24, 28, 32, 44, 48, 60, 68, 72, 80, 84, 88$. Using Paley Construction II we add $36=2(17+1)$, $52=2(25+1)$, $76=2(37+ …
- 1,245
4
votes
0
answers
140
views
Does an instance of this generalisation of the determinant exist?
Let $n$ be composite, $d$ a divisor greater than $1$ and $m=n/d$. Does anybody know if there is a general mapping $T$ from $n×n$ matrices to $m×m$ matrices that preserves the determinant? Over a field …
- 1,245
3
votes
Accepted
On the half-skew-centrosymmetric Hadamard matrices
Let $H_n$ be an $n×n$ Hadamard matrix and $R_n$ the $n×n$ reverse identity matrix.
The matrix $X= \begin{pmatrix}
H_n & R_nH_n \\
H_n & -R_nH_n
\end{pmatrix}$ has entries of length $1$ and $$XX^* = 2n …
- 1,245
1
vote
Reshaping data vector into a matrix for deconvolution using a circulant matrix
To circumvent the size difference between $S$ and $v$, one can use JPL codes. These are a XOR (which is modulo $2$ addition) of two or more maximal length sequences of coprime sizes.
After 2nd thought …
- 1,245