matrix multiplication

Matrix Multiplication, basic strategy

What does it mean to multiply one matrix by another? This is a really nice diagram that tells it all.

MatrixMult0' — from hem.libretexts.org. Calculations are shown for C11 and c22 of the result matrix.

This can be very confusing. Some kids will learn he pattern, no problem. Others will have trouble finding a place to store something in their head that has no apparent purpose.

Practical Matrix Multiplication

What does all of this mean in real life? We Adults use spread sheets with user supplied equations that allows them to do the same calculations over and over.

Let us take a gal Joan that sells home made pies: apple, black berry, and coconut

Joan lives in western Washington State. Apples are pretty inexpensive, black berries grow as a weed, and fresh coconut is expensive. Joan uses spread sheets to keep track of

how many pies she sells each day of the week
how much she sells them for
how much it costs to produce them.

Joan may multiply these two matrices just to view the revenue and the production cost for each type of pie and day of the week.

MatrixMult1 — A spread sheet from Joan’s kitchen. The first matrix has 3 columns and the second has 3 rows… we can multiply them.

Open Office Calc, the free, open source cousin of Microsoft Excel.

Let us do the math for the first and put it in B8. It is very easy to write in the wrong formulas. The software uses color coding to make it easy to visualize the math.

MatrixMult3 — The bottom matrix shows total earnings versus cost of production for each day without regard to the type of pie sold. Both matrices started out containing information on the type of pie. Note that the type of pie disappears from the product of the two matrices.

Entering each equation over and over is almost as PAINFUL as doing the entire beeping thing by hand. What is cool about these spread sheets is that they can be saved with all the equations. Joan can play around with production costs to see how they will affect day to day profits.

The EASY way to do Matrix Multiplication in Open Office

Open Office Calc has an easy way to calculate arrays.

In the upper left hand corner, click on the fx function key
Select the MMULT function
Enter the values. A matrix in columns B to D and rows 2 to 3 would be written as B2:D3. You don’t even have to type this in. Simply use the left mouse key to highlight these cells on your spread sheet.

Steps to doing matrix multiplication in Open Office Calc

Here are the results in the finished spread sheet. Compare the results of the matrix B12:F13 with the matrix in B8:F9.

MatrixMult5 — The Open Office matrix multiplication function (blue highlight) gives the same results as painstakingly entering the equations one by one.

Microsoft Office also performs the same calculations.

matrix multiplication