Let $$f (X) := \operatorname{Tr} \left( A (XAX)^{+} A \right)$$ I would like to find the gradient $\nabla_X f$.
I am puzzled by this. I cannot find a closed form. Could someone please give me hints or help me out?
2026-03-26 04:14:34.1774498474
Gradient of $X \mapsto \operatorname{Tr} \left( A (XAX)^{+} A \right)$
49 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in DERIVATIVES
- Derivative of $ \sqrt x + sinx $
- Second directional derivative of a scaler in polar coordinate
- A problem on mathematical analysis.
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Holding intermediate variables constant in partial derivative chain rule
- How would I simplify this fraction easily?
- Why is the derivative of a vector in polar form the cross product?
- Proving smoothness for a sequence of functions.
- Gradient and Hessian of quadratic form
Related Questions in MATRIX-CALCULUS
- How to compute derivative with respect to a matrix?
- Definition of matrix valued smooth function
- Is it possible in this case to calculate the derivative with matrix notation?
- Monoid but not a group
- Can it be proved that non-symmetric matrix $A$ will always have real eigen values?.
- Gradient of transpose of a vector.
- Gradient of integral of vector norm
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- How to differentiate sum of matrix multiplication?
- Derivative of $\log(\det(X+X^T)/2 )$ with respect to $X$
Related Questions in SCALAR-FIELDS
- Replace $X$ with $\mbox{diag}(x)$ in trace matrix derivative identity
- Derivative of bilinear form
- Index notation for vector calculus proof
- Gradient of $\mathbf{x} \mapsto(\mathbf a - \mathbf x)^\top\mathbf M^{-1}(\mathbf a-\mathbf x)$
- Recover scalar field from gradient
- Standard result for the gradient of a multidimensional Gaussian
- Visualizing a Scalar Field: $T(x,y,z)=10e^{-(x^2+y^2+z^2)}$
- Gradient of $X \mapsto \mbox{Tr}(AX)$
- Scalar fields whose gradient lies on a plane?
- What kind of projection does a specific map (3D -> 2D) correspond to?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?