Rotation matrix, worked example

It first introduces the reader to the fundamentals of experimental design. Systems theory, response surface concepts, and basic statistics serve as a basis for the further development of matrix least squares and hypothesis testing. The effects of different experimental designs and different models on the variance-covariance matrix and on the analysis of variance (ANOVA) are extensively discussed. Applications and advanced topics such as confidence bands, rotatability, and confounding complete the text. Numerous worked examples are presented. 

All of the matrices we have just worked out, as well as all others which describe the transformations of a set of orthogonal coordinates by proper and improper rotations, are called orthogonal matrices. They have the convenient property that their inverses are obtained merely by transposing rows and columns. Thus, for example, the inverse of the matrix... 

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