Purpose
Return value
Syntax
=MDETERM(array)
- array - A square array of numbers only.
Using the MDETERM function
The MDETERM function returns the matrix determinant of a given array , which must be a square matrix containing numbers only, and no empty values. In mathematics, the matrix determinant is a scalar value (single value) that is a function of the entries in a square matrix. The determinant is a special number that can help characterize some properties of the matrix. For example, if the determinant is zero, the matrix will not have an inverse.
The MDETERM function takes just one argument, array , which can be provided as a range or an array constant . Array must be a square matrix with the same numbers of rows and columns.
Examples
To get the matrix determinant for the 2 x 2 array shown in B7:C8, the formula in E7 is:
=MDETERM(B7:C8) // returns -1
The equivalent formula with an array constant is:
=MDETERM({4,3;3,2}) // returns -1
To get the matrix determinant for the 3 x 3 array shown in I7:K9, the formula in M7 is:
=MDETERM(I7:K9) // returns 1
The equivalent formula with an array constant is:
=MDETERM({1,0,5;2,1,6;3,4,0}) // returns 1
Notes
- The array argument must be a square matrix with an equal number of rows and columns
- The array argument can be provided as a range or array constant like {4,3;3,2}
- Empty cells or text in array will cause MDETERM to return a #VALUE! error
- MDETERM returns a #VALUE! if array does not have an equal number of rows and columns
Purpose
Return value
Syntax
=MINVERSE(array)
- array - A square array of numbers only.
Using the MINVERSE function
The MINVERSE function returns the inverse matrix of a given array. The product of a matrix and its inverse is the identity matrix , a n × n square matrix with ones on the main diagonal and zeros in every other position.
The MINVERSE function takes just one argument, array , which should be a square matrix, with an equal number of rows and columns. In order for MINVERSE to calculate an inverse matrix, array must contain numbers only. When an inverse exists, MINVERSE returns an inverse matrix with the same dimensions as the array provided.
If a matrix cannot be inverted, MINVERSE will return a #NUM! error. A matrix that can’t be inverted has a determinant of zero (0).
Examples
In the example shown the formula used in E7 to calculate the inverse matrix of the 2 x 2 matrix in the range B7:C8 is:
=MINVERSE(B7:C8) // returns {-2,3;3,-4}
The result is the 2 x 2 matrix seen in E7:F8, which can also be expressed as the array {-2,3;3,-4}.
The formula in M7 calculates the inverse matrix of the 3 x 3 matrix in B7:C8:
=MINVERSE(I7:K9) // returns {-24,20,-5;18,-15,4;5,-4,1}
The result is the 3 x 3 matrix seen in M7:O9, which can be expressed as the array {-24,20,-5;18,-15,4;5,-4,1}.
Array syntax
The MINVERSE function returns an array of values. In Excel 365 , where dynamic arrays are native , you can use the MINVERSE function without any special handling – MINVERSE will return an array of values that spill directly into cells in the worksheet.
In versions of Excel prior to Excel 365, you need to enter MINVERSE enter as a multi-cell array formula to display results directly on the worksheet. To do this, make a selection of the right size, and enter MINVERSE with control + shift + enter .
Notes
- The input array must be a square matrix with an equal number of rows and columns
- The array argument can be provided as a range or array constant like {4,3;3,2}
- Empty cells in the source array will cause MINVERSE to return the #VALUE! error
- MINVERSE returns the #VALUE! error value if array does not have an equal number of rows and columns.
- If a matrix cannot be inverted, MINVERSE will return a #NUM! error.
