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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 /math/matrices.org | |
parent | 561bac75579391c14e47eaccfabdf9eda98855da (diff) |
Diffstat (limited to 'math/matrices.org')
-rw-r--r-- | math/matrices.org | 32 |
1 files changed, 0 insertions, 32 deletions
diff --git a/math/matrices.org b/math/matrices.org deleted file mode 100644 index a7ba58b..0000000 --- a/math/matrices.org +++ /dev/null @@ -1,32 +0,0 @@ -#+TITLE:Matrix Properties -#+SETUPFILE: ../math_options.org -#+LATEX_HEADER: \usepackage{bm} -#+LATEX_HEADER: \usepackage{mathtools} - -* 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*} |