Talk:Alternating multilinear map: Difference between revisions - Wikipedia

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The linear case (a linear map V → W), is an alternating map by any sensible definition, as may be seen by the statement that every [[p-vector]] is alternating. The [[generalized Kronecker delta]] is a useful mechanism for producing a fully alternating tensor of any order, for example, but process this leaves scalars and order-1 tensors unchanged. I can imagine a reader seeking to answer the question "Is a vector alternating?" or "Is a linear map alternating?" Does anyone have language from a reference that allows us to naturally answer this question in the affirmative? —[[User_talk:Quondum|Quondum]] 22:43, 1 September 2016 (UTC)

:I rewrote the definition. From it follows that a linear map <math>f: V \to W</math> is alternating iff it meets the following condition:

::If <math>x</math> is linearly dependent then <math>f(x)=0</math>, which is equivalent to

::If <math>x=0</math> then <math>f(x)=0</math>

:

:Since this condition is always met one can deduce from the given definition of alternation that linear maps of the form <math>f: V \to W</math> are alternating. [[User:Bomazi|Bomazi]] ([[User talk:Bomazi|talk]]) 16:26, 29 April 2019 (UTC)

== Two adjacent elements or any two elements? ==