# Talk:Singular value

The definition of *singular value* given here is not general enough for the article singular value decomposition, since over there we need the concept for non-square matrices as well. AxelBoldt 16:41, 20 Apr 2005 (UTC)

## Contents

- 1 Why "singular"?
- 2 What is |A|?
- 3 S-number
- 4 singular value and operator norm
- 5 Chapter needed
- 6 Merge with Singular Value Decomposition
- 7 HIstory
- 8 In linear algebra... (proposal for new text to be inserted in the article)
- 9 s-number: redirect
- 10 "If T is self-adjoint, then the largest singular value s1(T) is equal to the operator norm of T"
- 11 In complex dynamics

## Why "singular"?

What's "singular" about a singular value? (Why the name?) —Ben FrantzDale 16:56, 20 November 2006 (UTC)

- According to my math prof, it's just that these are the values that make singular. —Ben FrantzDale 21:02, 5 December 2006 (UTC)

## What is |A|?

What is the meaning of |A| as mentioned in the article? --Drizzd (talk) 09:16, 4 April 2008 (UTC)

- I am told that |A| is in fact defined as , and therefore the previous formulation did not make any sense. I now expanded |A| to for the unitary diagonalization . can now be interpreted as either or as taking element-wise absolute value, because both give the same result. --Drizzd (talk) 20:37, 4 April 2008 (UTC)

## S-number

Who the hell calls them "s-number"? That's the first time I've heard the term. I'm moving this back to "Singular value". Swap (talk) 22:31, 3 May 2008 (UTC)

that s the first time i heard that too مبتدئ (talk) 17:27, 4 November 2008 (UTC)

## singular value and operator norm

I have a question: It is known that the max singular value is an operator norm (more precisly the one described here talks about the through the ||. ||2 induced operator Norm). Since the max singular value is a kind of strongest amplification of a system/ norm and since one can use different norms to define an induced operator norm, is the max singular value only limited or defined with the 2 induced norm or can one define it with any other norm???? Best regards مبتدئ (talk) 17:27, 4 November 2008 (UTC)

I mean max singular value is defined as:

with

now if i take another norm different from the 2 Norm, does this define a max singular value too??? thanks مبتدئ (talk) 17:37, 4 November 2008 (UTC)

other formulation of the question: the max singular value is the induced 2 norm of the operator. Is the induced infinity or the induced 5 norm of the operator also a/ the max singular value ??? مبتدئ (talk) 17:51, 4 November 2008 (UTC)

## Chapter needed

Can anyone add a chapter about what a structured singular value is? مبتدئ (talk) 01:40, 17 November 2008 (UTC)

## Merge with Singular Value Decomposition

Wouldn't it be better to merge this article with Singular Value Decomposition? It's far more complete and defines singular values in a much better way then this article does... anoko_moonlight (talk) 12:32, 20 January 2009 (UTC)

## HIstory

The history parts of this article do not agree with the Wikipedia entry Singular value decomposition. There we read that the term *singular value* was coined by Picard, while here the credit goes to Smithies. Who is right?

## In linear algebra... (proposal for new text to be inserted in the article)

In Linear Algebra, an eigenvalue and eigenvector of a square matrix A are a scalar λ and a nonzero vector x so that

A singular value and pair of singular vectors of a square or rectangular matrix A are a non-negative scalar σ and two nonzero vectors u and v so that

The superscript on ** stands for ***Hermitian transpose* and denotes the complex conjugate transpose of a complex matrix. If the matrix is real, then denotes the same matrix.

78.38.243.139 (21:15, 7 August 2011)

## s-number: redirect

Hello,

singular values are also called *s-numbers* as stated in the article, but s-number redirects to Meter Point Administration Number without any notice that singular value is also a valid meaning. Can someone with knowledge in the English Wikipedia (I only edit the German one regulary) add this?

Kind regards,

ThE cRaCkEr 14:25, 28 March 2012 (UTC) — Preceding unsigned comment added by ThE cRaCkEr (talk • contribs)

## "If T is self-adjoint, then the largest singular value s1(T) is equal to the operator norm of T"

Why does T have to be self-adjoint for max singular value to become operator norm?

, where

- You are right, removed the self-adjoint condition because it is unnecessary and really confusing. Yvanko55 (talk) 19:06, 3 August 2016 (UTC)

## In complex dynamics

There is also a notion of singular value in complex dynamics; namely for an entire holomorphic function f:\CC\to\CC, w\in\CC is a singular value iff it is a branch point of f as a covering, that is, for any neighbourhood V\in\CC of w, there is a component U_i of f^{-1}(V) so f is not injective on U_i. This notion should also be mentioned somewhere ...