Matrix calculus is about doing calculus, especially derivative and infinite series over spaces of vectors and matrices.

Can anyone explain the partial derivative below: $\\frac{\\partial a^tX^{-1}b}{\\partial X} = -X^{-t}ab^tX^{-t}$ I was trying to derive this equation using the below formula, but failed.

Aug 21, 2025 · The answer has to do with the definition of the gradient relative to the definition of the derivative/Jacobian matrix. Consider a smooth function f: Rn → R f: R n → R.

Nov 27, 2021 · Understanding numerator/denominator layout in matrix-calculus Ask Question Asked 4 years, 2 months ago Modified 2 years, 9 months ago

Oct 1, 2021 · Explore related questions calculus matrices derivatives matrix-calculus See similar questions with these tags.

This is why there are no dedicated courses on matrix calculus--there's nothing really new to the game. On Wikipedia you can scroll through seemingly endless formulas with derivatives of scalars with …

Dec 20, 2010 · What is the Jacobian matrix? What are its applications? What is its physical and geometrical meaning? Can someone please explain with examples?

Aug 2, 2017 · Does anyone have an insight on how to get better in matrix calculus (specially derivative with respect to vector or matrix) or how should I study such books? Thanks in advance.

18 Actually, we can directly calculate the derivate of a matrix starting from the definition of the derivate of functions.

Jan 10, 2021 · Explore related questions inner-products matrix-calculus chain-rule See similar questions with these tags.