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author | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
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committer | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
commit | 61b5ce20f25c5785e41574998a12c6d06eb05a5e (patch) | |
tree | 20e2225b4f30b15d8dee30351041d1f33d42b34a /src/math/matrices.org | |
parent | 561bac75579391c14e47eaccfabdf9eda98855da (diff) |
Diffstat (limited to 'src/math/matrices.org')
-rw-r--r-- | src/math/matrices.org | 33 |
1 files changed, 33 insertions, 0 deletions
diff --git a/src/math/matrices.org b/src/math/matrices.org new file mode 100644 index 0000000..c968f8c --- /dev/null +++ b/src/math/matrices.org @@ -0,0 +1,33 @@ +#+title:Matrix Properties +#+setupfile: ../../math_options.org + +* Disclaimer +This site as of now just a technology demonstration and its claims +should not be taken as true (even though I myself am pretty confident +they are) + +* Basic properties +\begin{align*} +A + B = B + A +\end{align*} + +* Dot product +\begin{align*} +(A^\text{T})^\text{T} &= A\\ +(A + B)^\text{T} &= A^\text{T} + B^\text{T}\\ +(AB)^\text{T} &= B^\text{T}A^\text{T} +\end{align*} + +* Transpose +\begin{align*} +\bm{a} \cdot \bm{b} &= \overline{\bm{b}} \cdot \bm{a}\\ +\bm{a} \cdot \bm{b} &= \bm{a}^\text{T} \bm{b} +\end{align*} + +* Hermitian transpose +\begin{align*} +A^\ast &= \left[\overline{a_{ij}}\right]\\ +(\lambda A)^\ast &= \left[\overline{\lambda a_{ij}}\right] = \overline{\lambda} \left[a_{ij}\right]^\ast = \overline{\lambda}\,\overline{A}\\ +A^\dag &= (A^\ast)^\text{T}\\ +A^{\dag\dag} &= A +\end{align*} |