## Enter the matrix… math

There is an entire class of functions in Excel that take things to a whole new level, and they are called matrices. Maybe you ran across this in math in school and have forgotten, maybe not, but the idea with a matrix is that it takes one grid of numbers of X x Y dimensions and uses operators to manipulate it using another grid of numbers that may or may not have the same dimensions.

The great part is that to use these functions in Excel, you don’t need to know any of that. Like I’ve mentioned before, it’s exactly like using a cookbook. Plug in the ingredients as specified, voila, the dish pops out the other end.

Maybe you’ve used the functions VLOOKUP and HLOOKUP, or maybe not, but they can be useful if you want to match exactly one criteria in a table and if the data you’re looking up is somewhere to the right of that criteria. So it’s perfect if you have something like a unique account number on the far left and want to use that to look up a name or phone number to the right of it:

`=VLOOKUP(M2,\$A1:\$L556,6,FALSE)`

This tells Excel to take the value in cell M2, compare it to all of the values in column A of the named range, then look up the value in the sixth column counting from the column defined in the second variable (in this case, F) where the first column is equal to M2. “FALSE” just means to use an exact match, whereas “TRUE” would mean to use an approximate match.

Again, this is great if you’re searching something with unique values in both places — there is only one account number, and only one data point associated with it.

Now what if you have multiple entries for the same person with different account numbers, or multiple sizes and colors of a product with differing prices, or you need to search on more than one data point in different columns, or your table was set up with the criteria you want to use somewhere to the right of the data points you’re searching?

Welcome, matrix functions! These are two nested commands that work miracles together. The first is INDEX, and what it basically does is point to a column with data that you’re going to pull stuff from, then follow that up with the criteria you’re going to use to do that. You can see the difference from the LOOKUP functions right off the bat, because those start with the single data point you’re going to use to search the data. The INDEX function starts with the place you’re going to get the answer from.

The MATCH function is the matrix math, and it allows you to specify multiple criteria matched to different columns in the source data. The nice part about it is that you can have as many different criteria as you need — first name, last name, account number; size, gender, color, style; title, author, binding, edition; and so on. And each of these can point to any particular bit of data you need — monthly cost, price, location, phone number, address, and so on. Any bit of data in the table can be found this way.

If you want to put a physical analogy on it, it’s this. LOOKUP functions are a librarian with a sliding ladder that moves horizontally or can be climbed vertically. But the way it works is that they first move it or climb it in the direction you specify until it hits the target word. Then, it slides or climbs the other direction however many rows or columns you specified, and has now targeted exactly one cell with the answer. Oh — and it can only move to the right or down from that initial search cell.

On the other hand, think of INDEX and MATCH as a whole bunch of librarians who have set out all over the same bookcases, but are simultaneously searching the rows and columns, and calling back and forth to each other to indicate what bits they’ve found that match.

If you work with any kind of inventory or any data sets where people’s info is broken down (as it should be) into separate first and last names and account identifiers, then you need to know these functions, because they will save you a ton of time. And the basic way they work is like this:

`INDEX(\$E1:\$E1405,MATCH(1,(W2=\$C\$1:\$C\$1405)*(X2=\$D\$1:\$D\$1405)*(AA2=\$J1:\$J1405),0))`

(Note: All column and row designations here are arbitrary and made up, so they don’t matter.)

That might look complicated, but it’s not. Let’s break it down. The first part, referring to the E column is the “Where” of the formula. That is, this is the column you’re pulling your data from. For example, if you want to use size, color, and style to find price, then this would be whatever column has the price data in it.

Next, we nest the MATCH function, and this lets INDEX know that what comes next will be the instructions it needs. The “1,” inside the parenthesis is a flag for MATCH, telling it to return one value. After that, each nested thing — and you can have as many as you need — follows the form “Single cell to look at equals column to search.” So, as seen here, for example, in the search data, column W might be the first name, and cell W2 is the cell corresponding to what we’re looking at. Meanwhile, column C in the target data includes first names, so what we’re saying is “Look for the single value of W2 down the entire column of C1 to C1405. The dollar signs are there to lock it as a fixed range.

All of the other parentheticals here follow the same pattern. Maybe X is the column for last name in the source and D is where the last names are in the target; and AA is account number, as is J.

The two other interesting things to note in building matrix equations: The single cell and the column are joined by an equals sign, not a comma, and this is important because, without it, your formula will break. What this tells Excel is that whatever the matrix pulls out of single cell must equal what’s in the column at that point.

The other thing to notice is that between the searches within parentheses, there aren’t commas, but rather asterisks, *, which indicate multiplication, and this is the heart of Matrix math.

What this tells the formula is to take the results of the first thingie, apply those criteria and pass it along to the second. In other words, if the first evaluation turned up nothing, that is mathematically a zero, and so it would quash anything coming from the second and third functions. On the other hand, if it comes up as a one, then whatever the second formula turns up will stay if there’s a one, dump if not, and then pass on to the third, fourth, etc..

Lather, rinse, repeat, for as many steps down the process you’ve created. A false result or zero at any point in the matrix math will kill it and result in nil. Meanwhile, as long as the tests keep turning up positives, what will fall out of the ass end of it is the honest legit “This data is the true data.”

Funny how that works, isn’t it? The only other trick you need to remember is that after you’ve entered this formula, you need to close it out by hitting Ctrl-Shift-Enter to let Excel know it’s a matrix formula. Then, if you want to copy it, you can’t use the usual Ctrl-C, Ctrl-V. Instead, you have to highlight the column with the formula at the top, then hit Ctrl-D. Voila… the whole thing duplicates down the column — which is what the “D” in the command stands for. To do the same thing across a row, the command is Ctrl-R, which you could think of as “repeat” or “replicate.”

And there you have it — a way to search multiple criteria in a row in order to find a specific data point in a table. You’re welcome.

But there’s more! One very important trick I’ve learned is how to avoid getting the dreaded “N/A#” in your results, because that totally breaks any summation you’re doing on the data. So I add an extra layer to the whole thing with a combination of the IF() and ISERROR() formulas.

This can make the thing really long, but worth it. I suggest entering the short INDEX formula first, make sure it’s working, and then use F2 to edit the cell, highlight everything and hit CTRL-C. Next, add “IF(ISERROR(” before the existing formula, move your cursor to the end, close out the ISERROR with a right parenthesis, “)”, then add comma, 0 (zero), and hit Ctrl-V to paste a copy of the original formal at the end. Close that with a final right paren.
The whole thing looks like this:

`IF(ISERROR(INDEX(\$E1:\$E1405,MATCH(1,(W2=\$C\$1:\$C\$1405)*(X2=\$D\$1:\$D\$1405)*(AA2=\$J1:\$J1405),0))),0,INDEX(\$E1:\$E1405,MATCH(1,(W2=\$C\$1:\$C\$1405)*(X2=\$D\$1:\$D\$1405)*(AA2=\$J1:\$J1405),0)))`

Sure, it gets a little long, but the advantage will be that if what you’re looking for isn’t in the source data, you’ll get a nice zero instead of an error message. And if you’re searching a text field, like size or name, then use “” instead of 0 after the ISERROR to get a blank cell.