diff options
Diffstat (limited to 'latex/know/concept/gram-schmidt-method/source.md')
| -rw-r--r-- | latex/know/concept/gram-schmidt-method/source.md | 5 |
1 files changed, 4 insertions, 1 deletions
diff --git a/latex/know/concept/gram-schmidt-method/source.md b/latex/know/concept/gram-schmidt-method/source.md index b0c7b3b..7920a30 100644 --- a/latex/know/concept/gram-schmidt-method/source.md +++ b/latex/know/concept/gram-schmidt-method/source.md @@ -4,7 +4,8 @@ # Gram-Schmidt method Given a set of linearly independent non-orthonormal vectors -$\ket*{V_1}, \ket*{V_2}, ...$ from a Hilbert space, the **Gram-Schmidt method** +$\ket*{V_1}, \ket*{V_2}, ...$ from a [Hilbert space](/know/concept/hilbert-space/), +the **Gram-Schmidt method** turns them into an orthonormal set $\ket*{n_1}, \ket*{n_2}, ...$ as follows: 1. Take the first vector $\ket*{V_1}$ and normalize it to get $\ket*{n_1}$: @@ -33,3 +34,5 @@ turns them into an orthonormal set $\ket*{n_1}, \ket*{n_2}, ...$ as follows: \end{aligned}$$ 4. Loop back to step 2, taking the next vector $\ket*{V_{j+1}}$. + +If you are unfamiliar with this notation, take a look at [Dirac notation](/know/concept/dirac-notation/). |