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authorPrefetch2021-02-24 09:54:20 +0100
committerPrefetch2021-02-24 09:54:20 +0100
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# 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/).