# sylvester: Solve Sylvester Equation In maotai: Tools for Matrix Algebra, Optimization and Inference

## Description

The Sylvester equation is of form

AX + XB = C

where X is the unknown and others are given. Though it's possible to have non-square A and B matrices, we currently support square matrices only. This is a wrapper of armadillo's sylvester function.

## Usage

 1 sylvester(A, B, C) 

## Arguments

 A a (p\times p) matrix as above. B a (p\times p) matrix as above. C a (p\times p) matrix as above.

## Value

a solution matrix X of size (p\times p).

## References

\insertRef

  1 2 3 4 5 6 7 8 9 10 11 12 13 ## simulated example # generate square matrices A = matrix(rnorm(25),nrow=5) X = matrix(rnorm(25),nrow=5) B = matrix(rnorm(25),nrow=5) C = A%*%X + X%*%B # solve using 'sylvester' function solX = sylvester(A,B,C) pm1 = "* Experiment with Sylvester Solver" pm2 = paste("* Absolute Error : ",norm(solX-X,"f"),sep="") pm3 = paste("* Relative Error : ",norm(solX-X,"f")/norm(X,"f"),sep="") cat(paste(pm1,"\n",pm2,"\n",pm3,sep=""))