By Alexey L. Pomerantsev
Delivering a simple clarification of the basics, tools, and purposes of chemometrics
• Acts as a pragmatic advisor to multivariate information research techniques
• Explains the equipment utilized in Chemometrics and teaches the reader to accomplish all appropriate calculations
• provides the elemental chemometric tools as worksheet services in Excel
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Extra info for Chemometrics in Excel
The converse is not true. For a joint distribution of multivariate random variables X1 , … , Xn , the covariance matrix C is defined by cij = cov(Xi , Xj ), i, j = 1, … , n This matrix plays the same role as the variance of a univariate distribution.
Nonbold italic characters indicate scalars and matrix elements, for example, X = (xij ). I and J denote the number of objects (samples) and variables, respectively; A denotes the number of latent variables (principal components). A corresponding small italic letter is used for the index, for example, i = 1, … , I. There are three special styles used to emphasize particular parts of the text. The menu style points out the text associated with computer interface, such as menu items and hot-key combinations.
These vectors correspond to the largest eigenvalues ????r of matrix At A, that is, At Aqr = ????r qr 38 MATRICES AND VECTORS DR = diag(????1 , … , ????R ) is a nonnegative definite diagonal matrix with elements ????1 ≥ … ≥ ????R ≥ 0 that are called singular values of matrix A. Singular values are equal to the square root of the eigenvalues of matrix At A ????r = √ ????r . An example of singular value decomposition (SVD) is shown in Fig. 24. By augmenting matrices PR and QR by orthonormal columns and matrix DR by zero entries, it is possible to construct matrices P (I × J), D (J × J), and Q (J × J) such that A = PR DR QtR = PDQt .