Optional. Type or paste the categories/species of each observation. For color-coding the plot.
#variables (rows): #observations per variable (columns):
Variables' statistics: variable# mean s
Covariance matrix: symmetric
Data centered at origin and scaled by SD, i.e. standardized:
Their statistics: should be 0 and 1 variable# mean s
Their Covariance matrix K (=correlation matrix):
Their eigenvalues λi, eigenvectors ei: Magnitudes |ei| of a square symmetric matrix: all eigenvectors are orthogonal, all eigenvalues are [non-negative?] real. DAMN: the math.js eigs() gives normed eigenvectors.... OK for PCs etc. that follows.
Loadings/weights: each PC row's α's i.e. NORMED eigenvalues λi, eigenvectors ei Magnitudes |ei| (=1)
standardized Covariance matrix times each normed eigenvector equals normed eigenvalue times normed eigenvector: Kei=λiei eigenvectors are only stretched by matrix (not any rotation) Sum of eigenvalues = sum of its matrix K's diagonal (its trace) Product of eigenvalues = det(matrix K)
Primary components Scores of standardized data:
X min: X max: Y min: Y max: