========================================================= Vector is physically "physical quantity" which has "size" and "direction". Vector is mathematically "notation" which express "over one number of numbers". Vector is generally expressed by one point in n dimensional space. ========================================================= In linear algebra, symbol for vector is used as bold lower case. Standard notation for feature vector is column vector. Direction of column vector is direction of "vertical downwards one arrow". ========================================================= Size of vector is called "norm" in linear algebra. Symbol for norm is pair of double vertical bars. $$$||x|| = \sqrt{x^{T}x} = \sqrt{x_{1}^{2}+x_{2}^{2}+...x_{N}^{2}}=\begin{bmatrix} \sum\limits_{k=1}^{N}x_{k}x_{k} \end{bmatrix} ^{\frac{1}{2}}$$$ $$$x^{T}x = \begin{bmatrix} x_{1}&x_{2}&...&x_{N} \end{bmatrix} \begin{bmatrix} x_{1}\\x_{2}\\...\\x_{N} \end{bmatrix}$$$ $$$x^{T}x=x_{1}^{2}+x_{2}^{2}+...x_{N}^{2}$$$ ========================================================= Unit vector has same direction with specific vector but length of unit vector is 1. $$$u = \frac{1}{||v||}v$$$ ====================================================================== Step of finding unit vector is called "normalization".