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Excel can perform operations — including arithmetic — on arrays of cells. Using this capability, you can perform complex computations with minimal effort. But of course, to use it, you must understand it.
An array in Excel is just a rectangular range of cells. You can perform any arithmetic operation on arrays, including addition, subtraction, multiplication, and division. You can also exponentiate — raise one array to the power of another array. Referring to the complete list of Excel’s operators, the table below shows the list of operators that support array computations.
In all of what follows, when an array (range) has 3 rows and 2 columns, we call it a “3x2 array” or “3x2 range”. An array or range with m rows and n columns is said to be an m x n or mxn array (range).

Before looking at the more exotic of these operators, let’s first understand how array arithmetic works.
Let’s start by looking at addition.
Let’s say that the array Aarray is in A1:B3, and that the array Barray is in D1:E3. The arrays are the same size and shape, 3x2, so the result will be 3x2. To compute the array sum of these two arrays, select a 3x2 range, say G1:H3. Then enter the formula
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Order "Spreadsheet Models for Managers, online edition, three months" by credit card, for USD 199.00 each, using our secure server, and receive download instructions by return email. 
Order "Spreadsheet Models for Managers, downloadable hyperbook edition" by credit card, for USD 199.00 each, using our secure server, and receive download instructions by return email. 
…<end snip>
Similarly, string concatenation also works. If we enter as an array formula
the resulting values are cellbycell concatenations of the values in the corresponding cells of the operand arrays.
Many worksheet functions, but not all, also support array computations. To determine which ones do and which don’t, you must perform experiments. We know of no place where this property is actually documented.
A common misuse of array formulas is what we call degenerate array formulas. A degenerate array formula is a formula entered into a single cell, and which always yields the same result as the identical formula entered into that same cell, but as a nonarray formula. For example, {=SUM(A1:A7)} entered into cell A8 is a degenerate array formula, because it always yields the same result as =SUM(A1:A7).
Last Modified: Wednesday, 27Apr2016 04:15:26 EDT
For many of you, matrix multiplication and array arithmetic are new ideas. It’s easy to get lost in the details of how they work and then forget about why we use them.
To keep a clear view of the forest and avoid focusing only on the trees, remember why we use matrix multiplication and array arithmetic. Briefly, we use them because we find that it’s very often helpful to decompose a problem into parts (analysis), then do calculations on the parts, and finally reassemble the final solution from the results of those partial calculations (synthesis).
Matrix multiplication and array arithmetic provide us with very convenient methods for performing those intermediate calculations on the parts. They’re the tools that make analysis and synthesis so powerful.