Hilbertova matrika
Hilbertova matríka [hílbertova ~] v linearni algebri je kvadratna matrika z elementi:
H
i
j
=
1
i
+
j
−
1
,
{\displaystyle H_{ij}={\frac {1}{i+j-1}\!\,,}
ki so vsi enotski ulomki .
Na primer H5 :
H
=
[
1
1
2
1
3
1
4
1
5
1
2
1
3
1
4
1
5
1
6
1
3
1
4
1
5
1
6
1
7
1
4
1
5
1
6
1
7
1
8
1
5
1
6
1
7
1
8
1
9
]
.
{\displaystyle H={\begin{bmatrix}1&{\frac {1}{2}&{\frac {1}{3}&{\frac {1}{4}&{\frac {1}{5}\\[4pt]{\frac {1}{2}&{\frac {1}{3}&{\frac {1}{4}&{\frac {1}{5}&{\frac {1}{6}\\[4pt]{\frac {1}{3}&{\frac {1}{4}&{\frac {1}{5}&{\frac {1}{6}&{\frac {1}{7}\\[4pt]{\frac {1}{4}&{\frac {1}{5}&{\frac {1}{6}&{\frac {1}{7}&{\frac {1}{8}\\[4pt]{\frac {1}{5}&{\frac {1}{6}&{\frac {1}{7}&{\frac {1}{8}&{\frac {1}{9}\end{bmatrix}\!\,.}
Hilbertove matrike so tipičen primer slabo pogojenih matrik, s katerimi je težko numerično računati. Determinanta zgornje matrike je približno
3
,
75
⋅
10
−
12
{\displaystyle 3,75\cdot 10^{-12}
Hankelova matrika .
The article is a derivative under the Creative Commons Attribution-ShareAlike License .
A link to the original article can be found here and attribution parties here
By using this site, you agree to the Terms of Use . Gpedia ® is a registered trademark of the Cyberajah Pty Ltd
![{\displaystyle H={\begin{bmatrix}1&{\frac {1}{2}&{\frac {1}{3}&{\frac {1}{4}&{\frac {1}{5}\\[4pt]{\frac {1}{2}&{\frac {1}{3}&{\frac {1}{4}&{\frac {1}{5}&{\frac {1}{6}\\[4pt]{\frac {1}{3}&{\frac {1}{4}&{\frac {1}{5}&{\frac {1}{6}&{\frac {1}{7}\\[4pt]{\frac {1}{4}&{\frac {1}{5}&{\frac {1}{6}&{\frac {1}{7}&{\frac {1}{8}\\[4pt]{\frac {1}{5}&{\frac {1}{6}&{\frac {1}{7}&{\frac {1}{8}&{\frac {1}{9}\end{bmatrix}\!\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d4fb8ebc50fc9e2442eae5b8ae805d44f10c55f3)
