I have the singular value decomposition of an image: $X = U \Sigma V^T$, where $\Sigma$ is diagonal matrix. I want to reformulate this equation like this: $X=\Sigma D$ where $D$ is any combination of $U$ and $V$. Is there efficient way for that???
2026-03-30 01:29:57.1774834197
Property of multiplation of a diagonal matrix
134 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in EIGENVALUES-EIGENVECTORS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Show that this matrix is positive definite
- Is $A$ satisfying ${A^2} = - I$ similar to $\left[ {\begin{smallmatrix} 0&I \\ { - I}&0 \end{smallmatrix}} \right]$?
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Question on designing a state observer for discrete time system
- Evaluating a cubic at a matrix only knowing only the eigenvalues
- Eigenvalues of $A=vv^T$
- A minimal eigenvalue inequality for Positive Definite Matrix
- Construct real matrix for given complex eigenvalues and given complex eigenvectors where algebraic multiplicity < geometric multiplicity
Related Questions in DIAGONALIZATION
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Show that $A^m=I_n$ is diagonalizable
- Simultaneous diagonalization on more than two matrices
- Diagonalization and change of basis
- Is this $3 \times 3$ matrix diagonalizable?
- Matrix $A\in \mathbb{R}^{4\times4}$ has eigenvectors $\bf{u_1,u_2,u_3,u_4}$ satisfying $\bf{Au_1=5u_1,Au_2=9u_2}$ & $\bf{Au_3=20u_3}$. Find $A\bf{w}$.
- Block diagonalizing a Hermitian matrix
- undiagonizable matrix and annhilating polynom claims
- Show that if $\lambda$ is an eigenvalue of matrix $A$ and $B$, then it is an eigenvalue of $B^{-1}AB$
- Is a complex symmetric square matrix with zero diagonal diagonalizable?
Related Questions in SVD
- Singular values by QR decomposition
- Are reduced SVD and truncated SVD the same thing?
- Sufficient/necessary condition for submatrix determinant (minor) that decreases with size?
- Intuitive explanation of the singular values
- SVD of matrix plus diagonal matrix and inversed
- Fitting a sum of exponentials using SVD
- Solution to least squares problem
- Are all three matrices in Singular Value Decomposition orthornormal?
- Solving linear system to find weights in $[0,1]$
- How to utilize the right-hand side in inverse problems
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?
You cannot rewrite the equation in that form. The reason there are matrices $U,V$ in the singular value decomposition is that in general one needs them in order to reduce "what remains" of $X$ to just a diagonal matrix, which is a very restricted form. With just a right-multiplication allowed, one cannot in general make this work with the diagonal matrix$~\Sigma$.