求一道矩阵题的具体解法设矩阵A和B满足关系式AB=A+2B,其中|423|A=|110|,求B|-123|

Question

求一道矩阵题的具体解法
设矩阵A和B满足关系式AB=A+2B,其中
| 4 2 3 |
A=| 1 1 0 | ,求B
| -1 2 3 |

Answer 1

这个方法需要用到矩阵的拉直
它是Lyapunov方程的一种特例
B=lyap(A,2*ones(3,3),-A)
就可以解决
B =
0.9061 -0.0939 -0.0939
-0.2723 0.7277 -0.2723
-0.1721 -0.1721 0.8279
LYAP Solve continuous-time Lyapunov equations.
X = LYAP(A,C) solves the special form of the Lyapunov matrix
equation:
A*X + X*A' = -C
X = LYAP(A,B,C) solves the general form of the Lyapunov matrix
equation (also called Sylvester equation):
A*X + X*B = -C