Tool to calculate the norm of a vector. The vector standard of a vector space represents the length (or distance) of the vector.

Vector Norm - dCode

Tag(s) : Matrix

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool to calculate the norm of a vector. The vector standard of a vector space represents the length (or distance) of the vector.

The norm of a vector is its length. If $ A $ and $ B $ are two points (of a space of $ n $ dimensions) then the norm of the vector, noted with a double bar $ \|\overrightarrow{AB}\| $ is the distance between $ A $ and $ B $ (the length of the segment $ [AB] $).

In a space of dimension $ n $, a vector $ \vec(v) $ of components $ x_i $ : $ \vec(v) = (x_1, x_2, ..., x_n) $ is computed by the formula: $$ \left\|\vec{v}\right\| = \sqrt{x_1^2 + x_2^2 + \cdots +x_n^2} $$

The norm of a vector can also be computed from the scalar product of the vector with itself: $ \| \vec{v} \| = \sqrt{ \vec{v} \cdot \vec{v} } $.

In the plane, for a vector $ \vec(v) = (x,y) $ the formula is simplified $ \|\vec{v}\|= \sqrt{x^2+y^2} $

Example: $ \vec(v) = \left( \begin{array}{c} 1 \ 2 \end{array} \right) $ so $ \|\vec(v)\| = \sqrt{1^2+2^2} = \sqrt{5} $

In space, for a vector $ \vec(v) = (x,y,z) $ the formula is simplified $ \|{\vec {v}}\|= \sqrt{x^2+y^2+z^2} $

From the coordinates of the points $ A (x_A,y_A) $ and $ B (x_B,y_B) $ of the vector $ \overrightarrow{AB} $, the components of the vector are $ {\overrightarrow {AB}} = (x_B-x_A), (y_B-y_A) $ and therefore the norm is $ \|\overrightarrow {AB}\| = \sqrt{(x_B-x_A)^2+(y_B-y_A)^2} $

dCode retains ownership of the source code of the script Vector Norm online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Vector Norm script for offline use on PC, iPhone or Android, ask for price quote on contact page !

norm,vector,length,value,absolute,space,vectorial,distance

Source : https://www.dcode.fr/vector-norm

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲