Algebra over Field/Examples
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Examples of Algebras over Fields
Vectors in $3$-Space with Cross Product
Let $V$ be the vector space formed of the set of all vectors in space.
Then $\struct {V, \times}$ forms an algebra over the field of vectors in space where $\times$ is the vector cross product.
$2 \times 2$ Matrices under Multiplication
The set of all $2 \times 2$ matrices with real or complex entries forms an algebra over the field of real numbers.