Chapter 3
... Theorem 3.4. For A an n × n matrix, the following are equivalent: (i) A is invertible; (ii) AX = 0n×1 has only the trivial solution X = 0n×1 ; (iii) the reduced row echelon form of A is In ; (iv) A is row equivalent to In ; (v) A can be written as a product of elementary matrices. Proof. We prove (i ...
... Theorem 3.4. For A an n × n matrix, the following are equivalent: (i) A is invertible; (ii) AX = 0n×1 has only the trivial solution X = 0n×1 ; (iii) the reduced row echelon form of A is In ; (iv) A is row equivalent to In ; (v) A can be written as a product of elementary matrices. Proof. We prove (i ...
ch1.3 relationship between IO and state space desicriptions
... Definition: Two time-invariant dynamical systems are said to be zero-state equivalent if and only if they have the same impulse response matrix or the same transfer function matrix. Theorem: Two equivalent LTI systems are zero-state equivalent. ...
... Definition: Two time-invariant dynamical systems are said to be zero-state equivalent if and only if they have the same impulse response matrix or the same transfer function matrix. Theorem: Two equivalent LTI systems are zero-state equivalent. ...
![[2012 solutions]](http://s1.studyres.com/store/data/008844911_1-801f2c6ec896db15646b0285c5651457-300x300.png)
