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This criterion, that is the ratio of the determinant of the within-cluster sums of squares and cross products matrix and that of the between clusters sums of squares and cross products matrix, is equivalent to the D-optimality criterion in the optimal design theory and related to minimization of the volume of the simultaneous confidence region of the cluster means.
To quantify this vector, I created a score for each specimen on the stream reservoir shape axis by multiplying the eigenvector of the habitat term's sums of squares and cross products matrix from a preparatory MANCOVA (final model same as above) by the shape variables block to yield a column of habitat divergence vector scores for each individual.
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Among the basic ones, we can find, e.g, vector scalings, inner (dot) products, matrix-vector products, solution of triangular systems, matrix matrix products, etc.
Prior to running the PCA, the elements of each cross-products matrix were "correlated" (centered and standardized by standard deviation) to remove magnitude differences among variables [37].
The three devices are all quite different, as the OEM differentiates its product matrix.
We want to reiterate that quite a while ago, a great matrix was drawn on the wall, with four quadrants in it [this product matrix].
The synthesis procedure is based on the operation of the separation product matrix representing the products.
Fig. 3 Interim stage of a TIM decomposition by product (matrix (mathbf{M}^{ip})).
First, several useful properties of the cross-product matrix will be given.
This is also captured as from the [1, 3] element of the product matrix.
This is captured by from the [1, 3] element of the product matrix.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com