M mult

MMULT Function

The MMULT function in Excel returns the matrix product of two arrays. The matrix product is the result of multiplying two matrices, where the number of columns in the first matrix must equal the number of rows in the second matrix.

Syntax:

MMULT(array1, array2)

• array1: The first matrix (array or range) to multiply.
• array2: The second matrix (array or range) to multiply.

The number of columns in array1 must be equal to the number of rows in array2.

Examples:

1. Matrix Product of 2x2 Matrices
   If the range A1:B2 contains:

   1   2  
   3   4  
   

   and C1:D2 contains:

   2   0  
   1   3  
   

   Formula: =MMULT(A1:B2, C1:D2)
   Returns:

   4   6  
   10  12  
   

   Explanation: Each element is the dot product of the corresponding row and column.

2. Matrix Product of a 2x3 and a 3x2 Matrix
   If A1:C2 contains:

   1   2   3  
   4   5   6  
   

   and D1:E3 contains:

   7   8  
   9   10  
   11  12  
   

   Formula: =MMULT(A1:C2, D1:E3)
   Returns:

   58   64  
   139  154  
   

   Explanation: Excel multiplies rows of the first matrix by columns of the second matrix.

Usage Notes:

• The number of columns in the first matrix must equal the number of rows in the second matrix; otherwise, Excel will return a #VALUE! error.
• The resulting matrix will have dimensions equal to the number of rows in array1 and the number of columns in array2.
• The MMULT function must be entered as an array formula in versions prior to Excel 365:
  • Select the output range with appropriate dimensions.
  • Enter the formula and press Ctrl + Shift + Enter.
• In Excel 365 and Excel 2021, dynamic arrays automatically spill the result.
• All elements in the arrays must be numeric; non-numeric values will result in a #VALUE! error.
• MMULT is widely used in fields like engineering, statistics, and data analysis for matrix multiplication and linear transformations.