Excel MMULT function

Excel provides functions for the manipulation of arrays or matrices TRANSPOSE(array) returns the transpose of an array, MDETERM(array) returns the matrix determinant of an array, MINVERSE(array) returns the matrix inverse of an array, MMULT(arrayl, array2) returns the matrix product of two arrays and SUMPRODUCT(arrayI, array2,. ..) returns the sum of the products of corresponding array elements. These functions are discussed more fully in Chapter 9. 

While the MINVERSE and MMULT functions are sufficient to solve well-posed linear systems, there are many more functions that can lead to more robust computations. A completely free Excel Add-On called Matrix.xla can be downloaded from the website http //digiIander.libero.it/foxes/SoftwareDownload.htm. In addition to the software, there is a comprehensive manual (in two volumes). Readers are encouraged to install this software on their own computer. Once Matrix.xla is installed, aU Excel applications have an enhanced set of functions available for matrix operations... 

In Figure 19-5, we enter the wavelengths in column A just to keep track of information. We will not use these wavelengths for computation. Enter the products eh for pure X in column B and eh for pure Y in column C. The array in cells B5 C6 is the matrix K. The Excel function MINVERSE(B5 C6) gives the inverse matrix, K-1. The function MMULT(matrix 1, matrix 2) gives the product of two matrices (or a matrix and a vector). The concentration vector, C, is equal to K 1 A, which we get with the single statement... 

Vector multiplication can be accomplished easily by the use of one of Excel s worksheet functions for matrix algebra, MMULT(inafr/x7, matrix2). For the matrices A and B defined above. 

Determining the inverse of a matrix by hand is a fairly complicated matter. Fortunately, Excel has a built-in function, MINVERSE, that will perform the inversion. It also has a matrix multiplication function, MMULT, that will calculate the product of two matrices. In order to let the spreadsheet know that your instructions concern an entire block or array rather than an individual cell, these two functions require that you first highlight the entire block to which the instruction applies, and then enter the instruction while simultaneously depressing Ctrl, Shift, and Enter. 

This exercise introduces two new features of the EXCEL software the matrix multiplication and transpose macros MMULT() and the TRANSPOSE(). These are best activated using the =/ icon on the TOOLBAR and the option to drag out the array data to be multiplied, visible in the function window. You select an equal area of blank cells on the spreadsheet and then activate the MMULT() or TRANSPOSEO macros. Note too that after selecting the particular area for each array, the sequence to enter these cell references requires CTL/SHIFT/ENTER. Otherwise, only one entry will appear in the top-left hand cell of the chosen active cells for the operation. 

As already sjiown in Sect. 4.2.2.5 the solution to the above equation can be obtained by = A -F, whereas the inversion of A and its multiplication with F may be performed with the help of standard PC-soflware. In EXCEL the respective matrix-functions to be used are MINV and MMULT. 

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