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Fredrik

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[tex]\|u\|=\sqrt{\langle u,u\rangle}[/tex]

is called the norm of u. A basis is said to be orthonormal if all its members have norm 1 and are orthogonal to each other, i.e. if

[tex]\langle x_i,x_j\rangle=\delta_{ij}[/tex]

where [itex]\delta_{ij}[/itex] is the Kronecker delta (=1 when i=j, and =0 otherwise).

Intuitively, you can think of this as meaning that the basis vectors all have length 1 and are perpendicular to each other, but we're really talking about generalizations of those concepts.

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