## Saturday, December 24, 2016

### Using Matrix Operators For Flips in Excel 2016

I've been using my free 30 day evaluation for Office 2016 to see what Excel 2016 is capable of doing. It was a little cumbersome at first but I'm starting to get the hang of it. Working with magic squares has proven to be a good motivator. I was able to get it to use matrix operators to some of the basic flips.

The basic tools are the matrices which I labeled Flip and HalfFlip. To show what these matrices do we start with the source matrix, S, and first multiply it on the left side by Flip with MMULT. The result is a matrix that is flipped along the columns. Multiplying S on the right flips the source along the rows. When HalfFlip multiplies S on the left the top and bottom halves are flipped along the columns. When it multiplies S on the right the left and right haves are flipped along the rows. The transpose function flips S leaving the 1-16 diagonal unchanged. The result is represented by ST. The flip leaving the 4-13 diagonal unchanged is accomplished by the series of operations, (S·Flip)T·Flip.

With Excel 2016 I find that it helps to keep track of what one is doing by labeling the matrices and displaying the formulas used with the FORMULATEXT( ) function.

P.S. Merry Christmas!