Algebraic definiton of dot/scalar product and vector product and what do they describe geometrically ?

Dot: scalar product of e*a is the component of a in the direction of the unit vector

also called

inner product: dot

enclosed angle phi

a x b gives the shown area (of the parallelogram spanned by a and b) and is called vector product or

outer product: right hand srew

Explain row and collum vectors.

How is the matrix product defined? Rule of transposition and determinants?

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