# ECE 515, 9.18

Covering course notes, 3.6-8 and 2-8-10.

• Peano-Baker series for fundamental matrices, – properties, convergence, role of commutativity;
• Solutions for forced systems for LTV systems;
• General classification of spaces of solutions of LTI;

• Inner products, norms,
• symmetric matrices, symmetric and antisymmetric parts of a matrix,

### 2 Responses to ECE 515, 9.18

1. Heng-Sheng Chang September 19, 2018 at 1:58 pm #

Course notes about the relation between det $G$ and the set of independent vectors $\{v_i\}_{i=1}^n$

Note that $G$ is the Gramian matrix $G=V^TV$, and $V=[v_1\ v_2\ \dots\ v_n]$.\\

$\{v_i\}$ is linear dependent\\
$\iff$ there exists a vector $c\neq0$ s.t. $\sum c_iv_i=0$\\
$\iff\ \exists\ c\neq0$ s.t. $=0\ \forall j$\\
$\iff\ \exists\ c\neq0$ s.t. $\sum c_i=0\ \forall j$\\
$\iff\ \exists\ c\neq0$ s.t. $Gc=0$\\
$\iff$ det $G=0$

• Heng-Sheng Chang September 19, 2018 at 2:25 pm #

not sure how to use this site… how to get a displayed equation?