My linear algebra book seems to give a different definition than Mathworld.com so I'll state it.(adsbygoogle = window.adsbygoogle || []).push({});

Ascalar productover a vectorial space V is a vectorial real function that to every pair of vectorsu,v, associates a real number noted (u|v) satisfying the 4 axioms...

1.

2.

3.

4.

A vectorial space of finite dimension with a scalar product is called aeuclidean space.

My question is the following: I don't like how that definition sounds. Is it equivalent to: "Let V be a vectorial space of finite dimension. If there exists a scalar product function over V, then V is called aeuclidean space." ?

P.S. does anyone knows a good website that teaches about diagonalisation of hermitian matrixes?

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# Euclidian space definition

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