Regarding SVD: Why is it called Singular Value and what does that value represent? And where does the SVD play a part in applications? Thank you
2026-03-26 06:10:33.1774505433
What does Singular value represent in the context of Singular Value Decomposition
137 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 SVD
- Singular values by QR decomposition
- Are reduced SVD and truncated SVD the same thing?
- Clarification on the SVD of a complex matrix
- 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 $[0,1]$
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?
Judging by Why the SVD is named so... it sounds like the terminology is mostly caused by historical baggage rather than it really having much mathematical significance.
Anyway, most applications are based on the property that $\sigma_n=\max_{\| x \|=1,x \perp v_1,\dots,v_{n-1}} \| Ax \|$. The right singular vectors $v_n$ are the corresponding maximizers (which aren't unique), while $Av_n=\sigma_n u_n$. Thus you find the direction in the domain that $A$ makes the biggest, then you search among vectors orthogonal to that for the direction in the domain that $A$ makes biggest, and so on. You can show from this definition that the $u_n$ are also mutually orthogonal, thus this provides an orthogonal coordinate system for the domain and in general a different orthogonal coordinate system for the codomain such that in this pair of systems $A$ is diagonal with nonnegative entries.