New posts in matrix-calculus

Dot product of the gradient of a function

calculus matrices multivariable-calculus matrix-calculus

Gradients of functions involving matrices and vectors, e.g., $\nabla_{w} w^{t}X^{t}y$ and $\nabla_{w} w^t X^tXw$

matrices multivariable-calculus derivatives matrix-calculus

If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$

linear-algebra matrices determinant matrix-equations matrix-calculus

Upper Bound on the entries of $A^n$, where $A \in M_d(\mathbb C)$ and $n\in \mathbb N$

linear-algebra matrices matrix-calculus

Gradient of $a^T X b$ with respect to $X$

matrices derivatives vector-analysis matrix-calculus scalar-fields

$AB=BA$ implies $AB^T=B^TA$ when $A$ is normal

linear-algebra matrices matrix-equations matrix-calculus

Derivatives of eigenvalues

matrices eigenvalues-eigenvectors matrix-calculus

Not understanding derivative of a matrix-matrix product.

calculus matrices derivatives matrix-calculus

Matrix exponential for Jordan canonical form

linear-algebra matrices exponential-function matrix-calculus jordan-normal-form

How to calculate the gradient of log det matrix inverse?

matrices derivatives matrix-calculus scalar-fields

Calculate $\frac{∂L}{∂A}$ given $\frac{∂L}{∂G}$, $D=(A-\iota\cdot B^T)\odot\iota\cdot C^T$, and $G=D \odot(\iota\cdot E^T)+\iota\cdot F^T$

partial-derivative vector-analysis matrix-calculus

Taking a derivative with respect to a matrix

multivariable-calculus derivatives normal-distribution matrix-calculus scalar-fields

Integral of matrix exponential

linear-algebra matrices definite-integrals matrix-calculus matrix-exponential

Derivative of Quadratic Form

matrices multivariable-calculus derivatives matrix-calculus quadratic-forms

Derivative of squared Frobenius norm of a matrix

matrices derivatives matrix-calculus least-squares scalar-fields

Vector derivative w.r.t its transpose $\frac{d(Ax)}{d(x^T)}$

calculus matrices multivariable-calculus matrix-calculus

Differentiation of inner product with matrices

calculus derivatives inner-products matrix-calculus multinomial-coefficients

Derivative of the nuclear norm

linear-algebra derivatives matrix-calculus nuclear-norm proximal-operators

Derivative of the inverse of a matrix

matrices derivatives inverse matrix-calculus

Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$

matrices derivatives matrix-calculus trace scalar-fields