The inner product of a vector with itself is the square of its norm/length.

Created almost 9 years ago, updated about 8 hours ago

By definition of the induced norm, $\|x\|^2=\langle x,x\rangle$. In standard coordinates this is the sum of squared absolute values. The identity links algebraic inner-product calculations to geometric lengths and supports the Pythagorean and Cauchy–Schwarz inequalities.

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