F4 (mathematics): Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Paolo328
I have extended the "See also" section
en>Connor Behan
m →top: - typo
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
In [[mathematics]], a [[map (mathematics)|mapping]] <math>f:V\to W</math> from a [[complex vector space]] to another is said to be '''antilinear''' (or '''conjugate-linear''' or '''[[semilinear transformation|semilinear]]''', though the latter term is more general) if


:<math>f(ax+by)=\bar{a}f(x)+\bar{b}f(y)</math>


for all ''a'', ''b'' in '''C''' and all ''x'', ''y'' in ''V'', where <math>\bar{a}</math> and <math>\bar{b}</math> are the [[complex conjugate]]s of ''a'' and ''b'' respectively. The [[composition (mathematics)|composition]] of two antilinear maps is complex-[[linear]].
Roberto is the name I love to be which is called with although it can be not the name on my birth certificate. I am a cashier. My colleagues say it's not good for me but precisely what I love doing is definitely to drive but I've been taking on brand-new things lately. My house is now in [https://www.Google.com/search?hl=en&gl=us&tbm=nws&q=Vermont&btnI=lucky Vermont]. I've been working on my website for some enough time now. Check it outdoors here: http://prometeu.net<br><br>my page clash of clans cheats ([http://prometeu.net mouse click the up coming post])
 
An antilinear map <math>f:V\to W</math> may be equivalently described in terms of the [[linear map]] <math>\bar f:V\to\bar W</math> from <math>V</math> to the [[complex conjugate vector space]] <math>\bar W</math>.
 
Antilinear maps occur in quantum mechanics in the study of [[T-symmetry|time reversal]] and in [[spinor calculus]], where it is customary to replace the bars over the basis vectors and the components of geometric objects by dots put above the indices.  
 
==References==
* Horn and Johnson, ''Matrix Analysis,'' Cambridge University Press, 1985. ISBN 0-521-38632-2. (antilinear maps are discussed in section 4.6).
* Budinich, P. and Trautman, A. ''The Spinorial Chessboard''. Spinger-Verlag, 1988. ISBN 0-387-19078-3. (antilinear maps are discussed in section 3.3).
 
== See also ==
*[[Linear map]]
*[[Complex conjugate]]
*[[Sesquilinear form]]
*[[Matrix consimilarity]]
*[[T-symmetry|Time reversal]]
 
[[Category:Functions and mappings]]
[[Category:Linear algebra]]

Latest revision as of 23:06, 11 December 2014


Roberto is the name I love to be which is called with although it can be not the name on my birth certificate. I am a cashier. My colleagues say it's not good for me but precisely what I love doing is definitely to drive but I've been taking on brand-new things lately. My house is now in Vermont. I've been working on my website for some enough time now. Check it outdoors here: http://prometeu.net

my page clash of clans cheats (mouse click the up coming post)

Retrieved from "https://en.formulasearchengine.com/index.php?title=F4_(mathematics)&oldid=227757"