Complex Matrices in Excel Format

On this webpage, we describe operations on complex number matrices where the matrices are represented as arrays of complex numbers in text format (i.e. the format used by Excel).

Worksheet Functions

Real Statistics Functions: The Real Statistics Resource Pack supplies the following array functions, where Y and Z are ranges that represent complex matrices and z is a text string that represents a complex (scalar) number.

ZMADD(Y, Z) = Y + Z	ZMSUB(Y, Z) = Y – Z
ZMMULT(Y, Z) = Y × Z	ZMMULTSCALAR(Y, z) = Y × z
ZMINVERSE(Z) = Z-1	ZMCONJUGATE(Z) = Z*
ZMDETERM(Z) = det(Z)

Note that functions equivalent to ZIdentity, ZTranspose, and ZIndex (see Complex Number Matrices) are not necessary since the standard Excel functions MUNIT, TRANSPOSE, and INDEX can be used with complex arrays whose elements are in Excel complex number format. For users of versions of Excel prior to Excel 2013, the Real Statistics function Identity can be used instead of MUNIT.

Just as the CMap and CText functions described in Complex Numbers can be used to translate between complex numbers in Excel format (text) and Real Statistics format (1×2 numeric arrays), the following functions provide similar support for complex matrices:

ZMap(Z): takes an array Z whose elements are complex numbers in Excel format and outputs an array in Real Statistics A+Bi format

ZText(Z): takes an array Z in A+Bi format and returns an equivalent array whose elements are in Excel complex number format

Real Statistics also supports an array version of the IMROUND function (described in Complex Numbers)

ZMROUND(Z, n): returns an array equivalent to Z but with each element rounded off to n decimal places.

Examples

Figure 1 shows a few examples of the use of these functions.

Figure 1 – Complex matrix operations

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Wolfram (2016) Complex matrix
https://mathworld.wolfram.com/ComplexMatrix.html

Brenner, S. C., Kaup, D. J. (1999) Introduction to complex numbers
No longer available online