Matrix calculus

Matrix differentiation

Derivative of linear equations

${\frac {d\;{\textbf {A}}{\textbf {x}}}{d\;{\textbf {x}}}}={\textbf {A}}^{T}$

${\frac {d\;{\textbf {x}}^{T}{\textbf {A}}}{d\;{\textbf {x}}}}={\textbf {A}}$

Derivative of quadratic equations

${\frac {d\;{\textbf {x}}^{T}{\textbf {A}}{\textbf {x}}}{d\;{\textbf {x}}}}=({\textbf {A}}^{T}+{\textbf {A}}){\textbf {x}}$

Derivative of matrix traces

${\frac {d\;trace\;{\textbf {A}}^{T}{\textbf {X}}{\textbf {B}}}{d\;{\textbf {X}}}}={\frac {d\;trace\;{\textbf {B}}{\textbf {X}}^{T}{\textbf {A}}}{d\;{\textbf {X}}}}={\textbf {A}}{\textbf {B}}$

External references

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