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Results tagged with linear-algebra
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user 5267
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
5
votes
A signature inequality?
Example found randomly:
EDIT: Make one with positive coefficients:
$A=\pmatrix{1&2&3\cr2&5&6\cr3&6&10}$ and
$B=\pmatrix{1&1&2\cr1&2&6\cr2&6&21}$.
EDIT: Here's how, with Magma
I get about a 25% proba …
- 2,704
2
votes
A signature inequality?
I get about 0.1% random in 3 for 4x4. Here is a "patterned" one:
[146 37 12 0]
[ 37 10 3 0]
[ 12 3 1 0]
[ 0 0 0 1]
[ 1 0 0 0]
[ 0 4221 202 -857]
[ 0 202 10 …
- 2,704
0
votes
A signature inequality?
Overnight search (about 25 million random 5x5) found:
[ 835 791 -119 -1 981]
[ 791 755 -113 0 931]
[-119 -113 17 0 -140]
[ -1 0 0 1 2]
[ 981 931 -140 2 1166]
[ 5 7 …
- 2,704
0
votes
A signature inequality?
Here is Magma code that will construct a 10x10 example, with one eigenvalue about +10 and nine of -1. Note that Magma has little numerical linear algebra, so I do it myself.
As can be seen in the fina …
- 2,704