return values - definition. What is return values
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%ما هو (من)٪ 1 - تعريف

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

return         
WIKIMEDIA DISAMBIGUATION PAGE
Return (programming); Returns; Returns (disambiguation); Return (album); Return (disambiguation); Return (film); Returning (disambiguation); RETURN; Return (song)
¦ verb
1. come or go back to a place.
(return to) go back to (a state or situation).
(especially of a feeling) come back after a period of absence.
Golf play the last nine holes in a round of eighteen holes.
2. give or send back or put back in place: return the lamb to the oven and add the olives.
feel, say, or do (the same feeling, action, etc.) in response.
(in tennis and other sports) hit or send (the ball) back to an opponent.
American Football intercept (a pass, kick, or fumble by the opposing team) and run upfield with the ball.
3. yield or make (a profit).
4. (of a judge or jury) state or present (a decision or verdict) in response to a formal request.
5. (of an electorate) elect (a person or party) to office.
6. Bridge lead (a card) after taking a trick.
7. Architecture continue (a wall) in a changed direction, especially at right angles.
¦ noun
1. an act or the action of returning.
(also return match or game) a second contest between the same opponents.
a thing which has been returned, especially an unwanted ticket for an event.
2. (also return ticket) Brit. a ticket allowing travel to a place and back again.
3. (also returns) a profit from an investment.
4. an official report or statement submitted in response to a formal demand: census returns.
Law an endorsement or report by a court officer or sheriff on a writ.
5. (also carriage return) a mechanism or key on a typewriter that returns the carriage to a fixed position at the start of a new line.
(also return key) a key pressed on a computer keyboard to simulate a carriage return.
6. an electrical conductor bringing a current back to its source.
7. Architecture a part receding from the line of the front, for example the side of a house or of a window opening.
Phrases
by return (of post) Brit. in the next available mail delivery to the sender.
many happy returns (of the day) a greeting to someone on their birthday.
Derivatives
returnable adjective
returner noun
Origin
ME: the verb from OFr. returner, from L. re- 'back' + tornare 'to turn'; the noun via Anglo-Norman Fr.
Return         
WIKIMEDIA DISAMBIGUATION PAGE
Return (programming); Returns; Returns (disambiguation); Return (album); Return (disambiguation); Return (film); Returning (disambiguation); RETURN; Return (song)
·noun That which is returned.
return         
WIKIMEDIA DISAMBIGUATION PAGE
Return (programming); Returns; Returns (disambiguation); Return (album); Return (disambiguation); Return (film); Returning (disambiguation); RETURN; Return (song)
I. v. n.
1.
Go or come back, get back, turn back.
2.
Recur, revert.
3.
Answer, reply, respond.
4.
Retort, recriminate.
5.
Revisit, come again.
II. v. a.
1.
Restore, give back, send back.
2.
Repay, refund.
3.
Requite, recompense, repay.
4.
Report, communicate, tell.
5.
Render, report, remit.
6.
Send, transmit, remit, convey.
III. n.
1.
Repayment, reimbursement, remittance, payment.
2.
Recompense, reward, requital, repayment, restitution.
3.
Advantage, benefit, profit, interest.
4.
Official account.

ويكيبيديا

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.