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, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

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 segment).

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 given for free. So if you need to download the online Vector Norm script for offline use, check contact page !

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

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

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback