multiple values - significado y definición. Qué es multiple values
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Qué (quién) es multiple values - definición

IN MATHEMATICS, THE SQUARE ROOT OF AN EIGENVALUE OF A NONNEGATIVE SELF-ADJOINT OPERATOR
Singular values; Singular Values
  • semi-axes]] of the ellipse.

Multiple abnormalities         
CONGENITAL ABNORMALITIES THAT AFFECT MORE THAN ONE ORGAN OR BODY STRUCTURE
Multiple congenital malformations; Multiple congenital anomalies
When a patient has multiple abnormalities (multiple anomaly, multiple deformity), they have a congenital abnormality that can not be primarily identified with a single system of the body or single disease process. Most medical conditions can have systemic sequelae, but multiple abnormalities occur when the effects on multiple systems is immediately obvious.
multiple unit         
  • A double decker [[Sydney Trains B set]]
  • River Line]]
  • Perth]] and the mining town of [[Kalgoorlie]] in [[Australia]].
  • Elektrichka on [[Yaroslavskiy Rail Terminal]], Moscow
  • RABe 523]] is the most common multiple units on Switzerland, used by almost every S-Bahn.
  • A [[N700 Series Shinkansen]] set in June 2008
  • South Side Elevated Railroad car #1—one of the cars that Frank Sprague converted to MU operation in Chicago
  • East Croydon}}
  • Simon's Town station]], [[Cape Town]]
TYPE OF TRAIN CONSISTING OF SELF-PROPELLED CARRIAGES CAPABLE OF COUPLING WITH OTHERS OF THE SAME OR SIMILAR TYPE
Multiple units; Multiple-unit; Self-powered; Motorized unit; Self-powered car; Multi-unit; Electric mutliple unit; Multiple Units; Multiple-unit car; Multiple Unit; Freight multiple unit; Multiple-unit operation; Multiple unit train; Multiple-Unit
¦ noun a passenger train of two or more carriages powered by integral motors which drive a number of axles.
Multiple unit         
  • A double decker [[Sydney Trains B set]]
  • River Line]]
  • Perth]] and the mining town of [[Kalgoorlie]] in [[Australia]].
  • Elektrichka on [[Yaroslavskiy Rail Terminal]], Moscow
  • RABe 523]] is the most common multiple units on Switzerland, used by almost every S-Bahn.
  • A [[N700 Series Shinkansen]] set in June 2008
  • South Side Elevated Railroad car #1—one of the cars that Frank Sprague converted to MU operation in Chicago
  • East Croydon}}
  • Simon's Town station]], [[Cape Town]]
TYPE OF TRAIN CONSISTING OF SELF-PROPELLED CARRIAGES CAPABLE OF COUPLING WITH OTHERS OF THE SAME OR SIMILAR TYPE
Multiple units; Multiple-unit; Self-powered; Motorized unit; Self-powered car; Multi-unit; Electric mutliple unit; Multiple Units; Multiple-unit car; Multiple Unit; Freight multiple unit; Multiple-unit operation; Multiple unit train; Multiple-Unit
A multiple-unit train or simply multiple unit (MU) is a self-propelled train composed of one or more carriages joined together, which when coupled to another multiple unit can be controlled by a single driver, with multiple-unit train control.

Wikipedia

Singular value

In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T : X Y {\displaystyle T:X\rightarrow Y} acting between Hilbert spaces X {\displaystyle X} and Y {\displaystyle Y} , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T T {\displaystyle T^{*}T} (where T {\displaystyle T^{*}} denotes the adjoint of T {\displaystyle T} ).

The singular values are non-negative real numbers, usually listed in decreasing order (σ1(T), σ2(T), …). The largest singular value σ1(T) is equal to the operator norm of T (see Min-max theorem).

If T acts on Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , there is a simple geometric interpretation for the singular values: Consider the image by T {\displaystyle T} of the unit sphere; this is an ellipsoid, and the lengths of its semi-axes are the singular values of T {\displaystyle T} (the figure provides an example in R 2 {\displaystyle \mathbb {R} ^{2}} ).

The singular values are the absolute values of the eigenvalues of a normal matrix A, because the spectral theorem can be applied to obtain unitary diagonalization of A {\displaystyle A} as A = U Λ U {\displaystyle A=U\Lambda U^{*}} . Therefore, A A = U Λ Λ U = U | Λ | U {\textstyle {\sqrt {A^{*}A}}={\sqrt {U\Lambda ^{*}\Lambda U^{*}}}=U\left|\Lambda \right|U^{*}} .

Most norms on Hilbert space operators studied are defined using s-numbers. For example, the Ky Fan-k-norm is the sum of first k singular values, the trace norm is the sum of all singular values, and the Schatten norm is the pth root of the sum of the pth powers of the singular values. Note that each norm is defined only on a special class of operators, hence s-numbers are useful in classifying different operators.

In the finite-dimensional case, a matrix can always be decomposed in the form U Σ V {\displaystyle \mathbf {U\Sigma V^{*}} } , where U {\displaystyle \mathbf {U} } and V {\displaystyle \mathbf {V^{*}} } are unitary matrices and Σ {\displaystyle \mathbf {\Sigma } } is a rectangular diagonal matrix with the singular values lying on the diagonal. This is the singular value decomposition.