# How to use the MMULT function

**What is the MMULT function?**

The MMULT function calculates the matrix product of two arrays, an array as the same number of rows as array1 and columns as array2.

### Table of Contents

## 1. MMULT Function Syntax

MMULT(*array1*, *array2*)

array1 |
Required. The first array of numbers you want to multiply. |

array2 |
Required. The second array of numbers you want to multiply. |

*"For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix has the number of rows of the first and the number of columns of the second matrix." Source: Wikipedia*

This function must be entered as an array formula.

## 2. Excel 365 dynamic arrays - spill values

Microsoft Excel has recently released an update to Excel 365 subscribers which allows you to use a new feature called dynamic array that replaces a regular array formula.

The image above shows the MMULT function in cell B12, however, it has been entered as a regular formula. Excel "knows" that it returns multiple values and automatically expands the range.

This is called "spilled array behavior" meaning the formula expands across cells automatically in order to show all values.

There is a blue border around the values from a spilled array but it will disappear as soon as you press with left mouse button on a cell outside the blue border. It reappears again if you press with left mouse button on any cell in the spilled array.

The following examples demonstrate how the function works.

## 3. Example 1

This example demonstrates cell ranges with an equal number of rows and columns.

Array1 (B2:C3) has **2** rows and array2 (E2:F3) has **2** columns, the returning array has **2** rows and **2** columns. Cell range B2:C3 and E2:F3 show the cell labels. Cell range H2:I3 shows the calculations made by the MMULT function in greater detail for each value in the array using the labels in B2:C3 and E2:F3.

Array formula in cell range L8:M9:

Cell L8: a11*b11+a12*b21 becomes 0*0+1*1 and returns 1.

Cell L9: a21*b11+a22*b21 becomes 1*0+0*1 and returns 0.

Cell M8: a11*b12+a12*b22 becomes 0*1+1*0 and returns 0.

Cell M9: a21*b12+a22*b22 becomes 1*1+0*0 and returns 1.

## 4. Example 2

This example demonstrates cell ranges with different numbers of rows and columns. Array1 (B2:C4) has **3** rows and array2 (E2:G3) has **3** columns, the returning array has **3** rows and **3** columns.

Array formula in cell range L8:M9:

Cell M8: a₁₁*b₁₁+a₁₂*b₂₁ becomes 0*1+1*4 and returns 4

Cell M9: a₂₁*b₁₁+a₂₂*b₂₁ becomes -4*1+0*4 and returns -4

Cell M10: a₃₁*b₁₁+a₃₂*b₂₁ becomes 3*1+1*4 and returns 7

Cell N8: a₁₁*b₁₂+a₁₂*b₂₂ becomes 0*2+1*-5 and returns -5

Cell N9: a₂₁*b₁₂+a₂₂*b₂₂ becomes -4*2+0*-5 and returns -8

Cell N10: a₃₁*b₁₂+a₃₂*b₂₂ becomes 3*2+1*-5 and returns 1

Cell O8: a₁₁*b₁₃+a₁₂*b₂₃ becomes 0*3+1*-6 and returns -6

Cell O9: a₂₁*b₁₃+a₂₂*b₂₃ becomes -4*3+0*-6 and returns -12

Cell O10: a₃₁*b₁₃+a₃₂*b₂₃ becomes 3*3+1*-6 and returns 3

## 5. Example 3

This example demonstrates cell ranges with different numbers of rows and columns, example 2. Array1 (B2:D3) has **2** rows and array2 (F2:G4) has **2** columns, the returning array has **2** rows and **2** columns.

Array formula in cell range L8:M9:

=MMULT(B8:D9,F8:G10)

Cell L8: a₁₁*b₁₁+a₁₂*b₂₁+a₁₃*b₃₁ becomes 1*0+2*-4+3*3 and returns 1

Cell L9: a₂₁*b₁₁+a₂₂*b₂₁+a₂₃*b₃₁ becomes 4*0+-5*-4+-6*3 and returns 2

Cell M8: a₁₁*b₁₂+a₁₂*b₂₂+a₁₃*b₃₂ becomes 1*1+2*0+3*1 and returns 4

Cell M9: a₂₁*b₁₂+a₂₂*b₂₂+a₂₃*b₃₂ becomes 4*1+-5*0+-6*1 and returns -2

## 6. Example 4

This example demonstrates how to calculate totals row-wise. The image above shows an array formula that returns an array containing the totals from each row in cell range C3:E7.

The number of columns in the first cell range or array must be equal to the number of rows in the second cell range or array.

Cell range C3:E7 has 3 columns and array {1; 1; 1} has three rows. The resulting array has the same number of rows as the cell range and the same number of columns as the array, in this case the array has 5 rows and 1 column. To be able to add all numbers in I use value 1 in the array.

You can also create an array that grows automatically based on the cell range, named range or an Excel defined Table.

This formula demonstrates how to create the array in the second argument using a cell range:

Let me explain this formula, the COLUMN function returns the corresponding column numbers from a cell range.

COLUMN(C3:E7) returns {3, 4, 5}.

COLUMN(C3:E7)^0 becomes {3, 4, 5}^0

and returns {1, 1, 1}. Any number (except zero) to the power of 0 (zero) returns 1. This array has values distributed across columns, we need them transposed row-wise.

TRANSPOSE(COLUMN(C3:E7)^0)

becomes TRANSPOSE({1, 1, 1}) and returns {1; 1; 1}.

This formula demonstrates how to create the array using a named range:

*named_range*, TRANSPOSE(COLUMN(

*named_range*)^0))

This formula demonstrates how to create the array using a reference to an Excel Table:

If you are an Excel 365 subscriber you can use the newly added SEQUENCE function:

## 7. Example 5

This example demonstrates how to calculate totals column-wise. This formula adds numbers and returns sums for each column in one calculation.

This article demonstrates how to search a data set with multiple strings using the MMULT function:

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### Functions in 'Math and trigonometry' category

The MMULT function function is one of 61 functions in the 'Math and trigonometry' category.

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### 4 Responses to “How to use the MMULT function”

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A great write-up as usual Oscar. Do you have any use cases to share? In 10 years of using Excel I can only think of one time where it occurred to me to use MMULT, and I can't put my finger on it now.

Hi Oscar,

Thanks for taking the request..

@ Andy.. & @Oscar

In addition.. to the previous discussion.. :)

Check the attached file.. there are few sample use of MMULT..

https://dl.dropboxusercontent.com/u/78831150/Excel/Sample%20use%20of%20MMULT.xlsx

https://dl.dropboxusercontent.com/u/78831150/Excel/Sample%20use%20of%20MMULT.jpg

https://postimg.org/image/tn0pfedvl/

Regards,

Deb

Andy,

Thank you. I have no examples to share, yet. I searched excelforum.com and found a few posts but nothing really sensational.

I googled "use of matrix multiplication" and found some practical examples in math and physics.

Deb,

Thank you for your contribution!

Formula #1=SUM(MMULT(B2:C15;{1;-1}))

MMULT(B2:C15;{1;-1}) returns {29; 77; -1; 27; 69; 3; -3; 32; 54; -67; -65; -46; 21; -67}

equivalent to =B2:B15-C2:C15

So this formula does the same thing: =SUM(B2:B15-C2:C15)

Formula #2=SUM(MMULT(B2:C15;{1;1})) sums of all values in B2:C15.

It is equivalent to this formula =SUM(B2:C15)

Good examples, I am beginning to understand. But I want to do someting creative and unique with the MMULT function, something that is not possible with other function or at least complicated to accomplish.

Thanks again for sharing!

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