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My linear algebra book seems to give a different definition than Mathworld.com so I'll state it.
A scalar product over a vectorial space V is a vectorial real function that to every pair of vectors u, v, associates a real number noted (u|v) satisfying the 4 axioms...
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A vectorial space of finite dimension with a scalar product is called a euclidean 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 a euclidean space." ?
P.S. does anyone knows a good website that teaches about diagonalisation of hermitian matrixes?
A scalar product over a vectorial space V is a vectorial real function that to every pair of vectors u, 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 a euclidean 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 a euclidean space." ?
P.S. does anyone knows a good website that teaches about diagonalisation of hermitian matrixes?