Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion
This paper describes a simple method to calculate the invers of a complex matrix. The key element of the method is to use a matrix inversion, which is available and optimised for real numbers. Some actual libraries used for digital signal processing only provide highly optimised methods to calculate the inverse of a real matrix, whereas no solution for complex matrices are available, like in [1]. The presented algorithm is very easy to implement, while still much more efficient than for example the method presented in [2]. [1] Visual DSP++ 4.0 C/C++ Compiler and Library Manual for TigerSHARC Processors; Analog Devices; 2005. [2] W. Press, S.A. Teukolsky, W.T. Vetterling, B.R. Flannery; Numerical Recipes in C++, The art of scientific computing, Second Edition; p52 : “Complex Systems of Equations”;Cambridge University Press 2002.
Summary
This paper describes a practical algorithm that converts the inversion of a complex matrix into an equivalent real matrix inversion so that highly optimized real-number routines can be used. Readers will learn a simple, implementation-friendly method that is more efficient than many naive complex inversion approaches and suited to DSP libraries that lack native complex inversion.
Key Takeaways
- Transform complex matrices into a structured real 2x2 block form to enable real-matrix inversion.
- Leverage optimized real matrix inversion libraries (e.g., BLAS/LAPACK or vendor DSP libs) to compute complex inverses.
- Reduce computation and implementation complexity compared with element-wise complex inversion methods.
- Adapt the approach for fixed-point or real-time DSP environments where only real routines are available.
Who Should Read This
DSP and communications engineers or numerical computing practitioners who need efficient complex-matrix inversion implementations and want to exploit optimized real-number libraries.
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