Chemometrics in Excel by Alexey L. Pomerantsev
By Alexey L. Pomerantsev
Delivering a simple rationalization of the basics, equipment, and purposes of chemometrics
• Acts as a realistic advisor to multivariate facts research techniques
• Explains the tools utilized in Chemometrics and teaches the reader to accomplish all correct calculations
• offers the fundamental chemometric tools as worksheet services in Excel
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Additional resources for Chemometrics in Excel
2. 3. 4. 5. 2 General Statistic Packages 1. 2. 3. 4. 5. 6. 3 Free Ware 1. 2. 3. 4. info/ 19 PART II THE BASICS 5 MATRICES AND VECTORS This chapter summarizes the main facts of the matrix and vector algebra, which are used in chemometrics. The text cannot serve as a textbook on matrix algebra; it is rather a synopsis, a brief guide to the field. A deeper and more systematic exposition can be found in the literature presented in Chapter 4. The text is divided into two parts named as The basics and Advanced information.
6) is used for matrix multiplication. 5 Matrices product. 6 The element of matrices product. 4 Square Matrix If the number of columns is equal to the number of rows (I = J = N), then the matrix is said to be a square matrix. In this section, only square matrices are considered. Among them there are matrices with special properties. An identity matrix (denoted by I and, sometimes, by E) is a matrix whose elements equal zero, except for the diagonal elements, which are equal to 1, for example ⎡1 ⎢0 I=⎢ … ⎢ ⎣0 0 1 … 0 … 0⎤ … 0⎥ … 0⎥ ⎥ 0 1⎦ It is obvious that AI = IA = A.
26 for illustration. 26 Projection on a subspace. 27 Projection. The projected vector y|| can be represented as the result of application of the projection matrix P y|| = Py. The projection matrix is defined by P = X(Xt X)−1 Xt . An example is shown in Fig. 27. 6 STATISTICS This chapter presents mathematical statistics, namely the main statistical methods that are used in chemometrics. The text below cannot serve as a textbook on statistics; it is rather a synopsis, a brief guide to mathematical statistics.