Chemometrics in Excel by Alexey L. Pomerantsev

By Alexey L. Pomerantsev

Offering a simple clarification of the basics, equipment, and purposes of chemometrics
• Acts as a pragmatic advisor to multivariate information research techniques
• Explains the tools utilized in Chemometrics and teaches the reader to accomplish all proper calculations
• provides the fundamental chemometric tools as worksheet features in Excel

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When the type of a vector is not specified, a column vector is implied. We will also follow this rule. Vectors are denoted by bold lower case letters. A zero vector is a vector whose elements are zeros. It is denoted by 0. 7 Simple Vector Operations Vectors can be added and multiplied by a number in the same way as it is done with matrices. An example is shown in Fig. 12. Two vectors x and y are said to be collinear if there exists a number ???? such that ????x = y. 8 Vector Products Two vectors x = (x1 , x2 , … , xN )t and y = (y1 , y2 , … , yN )t of the same dimension N can be multiplied.

L. Eriksson, E. Johansson, N. Kettaneh-Wold, S. Wold. Multi- and Megavariate Data Analysis, Umetrics, Umeå, 2001. 7. D. Brown, R. Tauler, B. Walczak. Comprehensive Chemometrics. Chemical and Biochemical Data Analysis, vol. 4 set, Elsevier, Amsterdam, 2009. 8. R. J. B. Seasholtz. , 1998. JOURNALS 17 9. J. Adams. Chemometrics in Analytical Spectroscopy, RSC, Cambridge, UK, 1995. 10. W. W. Zweinziger, S. Geiß. Chemometrics in Environmental Analysis, Wiley-VCH, Weinheim, 1997. 11. H. Mark, J. Workman.

4 Matrix transpose. by the t index, At . Formally, if A = {aij , i = 1, … , I; j = 1, … , J}, then At = {aji , j = 1, … , J; i = 1, … , I}. An example is shown in Fig. 4. Obviously, (At )t = A, (A + B)t = At + Bt . 5) is used to transpose a matrix. 3 Matrices Multiplication Matrices can be multiplied but only when they have corresponding dimensions, that is, the number of columns of A matches the number of rows of B. The product of matrix A (dimension I × K) and matrix B (dimension K × J) is matrix C (dimension I × J), whose elements are defined by K ∑ cij = aik bkj .

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