Editing Principal component analysis (section)

== Table of symbols and abbreviations ==

{| class="wikitable"
|-
! Symbol
! Meaning
! Dimensions
! Indices
|-
| <math>\mathbf{X} = [ X_{ij} ]</math>
| data matrix, consisting of the set of all data vectors, one vector per row
| <math> n \times p</math>
| <math> i = 1 \ldots n </math> <br /> <math> j = 1 \ldots p </math>
|-
| <math>n </math>
| the number of row vectors in the data set
| <math>1 \times 1</math>
| ''scalar''
|-
| <math>p </math>
| the number of elements in each row vector (dimension)
| <math>1 \times 1</math>
| ''scalar''
|-
| <math>L </math>
| the number of dimensions in the dimensionally reduced subspace, <math> 1 \le L \le p </math>
| <math>1 \times 1</math>
| ''scalar''
|-
| <math>\mathbf{u} = [ u_j ]</math>
| vector of empirical [[mean]]s, one mean for each column ''j'' of the data matrix
| <math> p \times 1</math>
| <math> j = 1 \ldots p </math>
|-
| <math>\mathbf{s} = [ s_j ]</math>
| vector of empirical [[standard deviation]]s, one standard deviation for each column ''j'' of the data matrix
| <math> p \times 1</math>
| <math> j = 1 \ldots p </math>
|-
| <math>\mathbf{h} = [ h_i ]</math>
| vector of all 1's
| <math> 1 \times n</math>
| <math> i = 1 \ldots n </math>
|-
| <math>\mathbf{B} = [ B_{ij} ]</math>
| [[Standard deviation|deviations]] from the mean of each column ''j'' of the data matrix
| <math> n \times p</math>
| <math> i = 1 \ldots n </math> <br /> <math> j = 1 \ldots p </math>
|-
| <math>\mathbf{Z} = [ Z_{ij} ] </math>
| [[z-score]]s, computed using the mean and standard deviation for each column ''j'' of the data matrix
| <math> n \times p</math>
| <math> i = 1 \ldots n </math> <br /> <math> j = 1 \ldots p </math>
|-
| <math>\mathbf{C} = [ C_{jj'} ] </math>
| [[covariance matrix]]
| <math> p \times p </math>
| <math> j = 1 \ldots p </math> <br /><math> j' = 1 \ldots p </math>
|-
| <math>\mathbf{R} = [ R_{jj'} ] </math>
| [[correlation matrix]]
| <math> p \times p </math>
| <math> j = 1 \ldots p </math> <br /><math> j' = 1 \ldots p </math>
|-
| <math> \mathbf{V} = [ V_{jj'} ] </math>
| matrix consisting of the set of all [[eigenvectors]] of '''C''', one eigenvector per column
| <math> p \times p </math>
| <math> j = 1 \ldots p </math> <br /><math> j' = 1 \ldots p </math>
|-
| <math>\mathbf{D} = [ D_{jj'} ] </math>
| [[diagonal matrix]] consisting of the set of all [[eigenvalues]] of '''C''' along its [[principal diagonal]], and 0 for all other elements ( note <math>\mathbf{\Lambda}</math> used above )
| <math> p \times p </math>
| <math> j = 1 \ldots p </math> <br /><math> j' = 1 \ldots p </math>
|-
| <math>\mathbf{W} = [ W_{jl} ] </math>
| matrix of basis vectors, one vector per column, where each basis vector is one of the eigenvectors of '''C''', and where the vectors in '''W''' are a sub-set of those in '''V'''
| <math> p \times L</math>
| <math> j = 1 \ldots p </math> <br /><math> l = 1 \ldots L</math>
|-
| <math>\mathbf{T} = [ T_{il} ] </math>
| matrix consisting of ''n'' row vectors, where each vector is the projection of the corresponding data vector from matrix '''X''' onto the basis vectors contained in the columns of matrix '''W'''.
| <math> n \times L</math>
| <math> i = 1 \ldots n </math> <br /><math> l = 1 \ldots L</math>
|}