inverse of a matrix wrong??

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Giovanni Salviati
评论： Walter Roberson 2019-9-8
Hello community,
I've just written this code:
close all
clear all
clc
s = tf('s');
A = [0 , 1 ; -2 , -3]
B = [1 ; 0]
I = [1 , 0 ; 0 , 1]
L = s*I-A;
Linv = inv(L)
and it's not equal to my counts that I've done on the paper; infact the L matrix should be
s+3/(s^2+3*s+2) 1/(s^2+3*s+2)
-2/(s^2+3*s+2) s/(s^2+3*s+2)
while in matlab the last fraction ( row 2 , column 2) is: (s + 8.438e-15)/(s^2+3*s+2)

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回答（1 个）

Walter Roberson
Walter Roberson 2019-9-7
It is not wrong, but it is subject to round-off error; it also is not being simplified.
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Giovanni Salviati
Giovanni Salviati 2019-9-8
编辑：Giovanni Salviati 2019-9-8
Ok solved it.
I've just written "syms s", instead of "s = tf('s')"
but i don't get it why with the second function it doesn't work
Walter Roberson
Walter Roberson 2019-9-8
The underlying code for tf and ss systems works with pure numeric matrices, and those have round off errors in calculations of matrix inverse. Matrix inverse numeric calculations are not done according to the formal definition of matrix inverse, because those calculations can take a long time.

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