CANOCO is widely used for PCA, CA, and canonical analysis. See note at end of Section 11.0.

Matrix Q is computed following eq. 9.32:

and matrix Q following eq. 9.40:

(1) 0.26726 0.28868 0.53452

(2) 0.28571 0.46291 0.28571

The eigenvalues of Q'Q are = 0.09613 (70.1%), X2= 0.04094 (29.9%), and X3 = 0 (because of the centring). The first two eigenvalues are also eigenvalues of Q'Q , its third eigenvalue being 1 (because Q is not centred; eq. 9.40). The normalized eigenvectors of Q'Q , corresponding to and ^2, are (in columns):

The third eigenvector is of no use and is therefore not given. Most programs do not compute it.

In scaling type 1 (Fig. 9.16a), the states in the rows of the data matrix (1, 2, 3, called "rows" hereinafter), whose coordinates will be stored in matrix F, are to be plotted at the centroids of the column states (0, +, ++, called "columns" hereinafter). The scaling for the columns is obtained using eq. 9.41:

(0) 0.78016 -0.20336 U = (+) -0.20383 0.81145 (++) -0.59144 -0.54790

The normalized eigenvectors of QQ' are (in columns):

(0) -0.53693 -0.55831 U = (+) -0.13043 0.79561 (++) 0.83349 -0.23516

(0) 1.31871 -0.34374 V = D (p+j)-1/2 U = (+) -0.37215 1.48150 (++) -0.99972 -0.92612

To put the rows (matrix F) at the centroids of the columns (matrix V), the position of each row along an ordination axis is computed as the mean of the column positions, weighted by the

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