MathLiveEuclidean norm
Gives the length of a vector as the square root of the sum of the squared magnitudes of its components. It is used to measure distance from the origin and in nearly all areas involving vectors.
\|\boldsymbol{x}\| = \sqrt{\sum_{i=1}^{n} |x_i|^2}What the symbols mean
| vector with components x_1, ..., x_n (real or complex) | |
| Euclidean norm (length) of the vector | |
| i-th component of the vector | |
| absolute value (magnitude) of the i-th component | |
| dimension of the vector space |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledEuclidean length, L2 norm, L²-norm, length of a vector, magnitude of a vector, norm of a vector formula
- SourceWikidata Q20076640
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