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Definition: The length (or norm) of a vector v = [v_1, v_2, … , v_n] in R^n is the non-negative scalar ||v|| defined by ||v|| = sqrt(v * v) = sqrt[(v_1)^2 + (v_2)^2 + ... + (v_n)^2].
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)