Category:Zero Vector Space Product iff Factor is Zero

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This category contains pages concerning Zero Vector Space Product iff Factor is Zero:


Let $F$ be a field whose zero is $0_F$ and whose unity is $1_F$.

Let $\struct {\mathbf V, +, \circ}_F$ be a vector space over $F$, as defined by the vector space axioms.

Let $\mathbf v \in \mathbf V, \lambda \in F$.


Then:

$\lambda \circ \mathbf v = \bszero \iff \paren {\lambda = 0_F \lor x = \bszero}$

Pages in category "Zero Vector Space Product iff Factor is Zero"

The following 3 pages are in this category, out of 3 total.