Talk:Matrix differential equation

Solved example of a matrix ODE

In this example, the equation is given as:

${\frac {dy}{dt}}=3y-4z,\quad {\frac {dz}{dt}}=4y-7z.$

but later there is a condition $x(0)=0$. What is "x" in this equation? If we are looking for $y$ and $z$, then there is no $x$, since $t$ is the variable of $y$ and $z$. Perhaps in the beginning it was $x$ and $y$ we were looking for, but by following edits they turned into $y$ and $z$? --Дарко Максимовић (talk) 18:14, 8 April 2009 (UTC)

Repeated eigenvalues

It seems this page could go into more detail regarding higher order systems and repeated eigenvalues. For example, the following addresses these issues: http://tutorial.math.lamar.edu/Classes/DE/HOSystems.aspx Twelvefifths (talk) 22:16, 20 July 2015 (UTC)

Stability and steady state of the matrix system

WARNING. The recipe given in this section leads to wrong results. The final statements are only true if x* is a particular solution of the complete equation. In general it is not. This section needs to be fixed by a mathematician. Unsigned by User:2804:14c:41:809b:a9fa:b140:4c5b:cb49

Duh!? Done. read the English? Cuzkatzimhut (talk) 15:35, 5 March 2019 (UTC)

Sorry! It continues wrong. A mathematician should closely look at it. — Preceding unsigned comment added by 2804:14C:41:809B:A9FA:B140:4C5B:CB49 (talk) 19:56, 5 March 2019 (UTC) x*, as defined, is NOT a solutiomn of the given system when A,b are not constants.

I think you are misreading it. In the lede, it was already established that A indicates a constant matrix, and likewise for b, when an argument (t) is omitted. There, here, and in the rest of the article, the respective cases are adequately demarcated for the well meaning reader. Cuzkatzimhut (talk) 21:57, 5 March 2019 (UTC)

NO! In the leading line, it is written A(t). It would help stressing in this section that A,b are constants. It is correct and it would help the readers to avoid a misinterpretation. — Preceding unsigned comment added by 2804:14C:41:809B:E19F:D943:9B65:A89A (talk) 00:08, 6 March 2019 (UTC)

The "only if" part regarding the eigenvalues of A with negative real part is wrong. You can have A with zero eigenvalues and still have a stable solution. — Preceding unsigned comment added by 2A0C:5A82:2305:4100:E4C9:6DAA:7E40:49A2 (talk) 15:36, 9 March 2024 (UTC)

Time dependent $\mathbf {b} (t)$

As in if the matrix equation is

$\mathbf {\dot {x}} (t)=\mathbf {Ax} (t)+\mathbf {b} (t)$

Solution process? — Preceding unsigned comment added by CH3APlayer (talk • contribs) 9:53, 19 April 2021 (UTC)

Duplicate?

This whole article looks like a duplicate of Linear dynamical system.

Moreover, it seems that a more standard meaning of "matrix differential equation" is actually an ordinary differential equation in a space of matrices; see https://encyclopediaofmath.org/wiki/Matrix_differential_equation. — Preceding unsigned comment added by Odulon (talk • contribs) 20:03, 25 January 2022 (UTC)