From b42f600599376917ee4f995298334875144e4d35 Mon Sep 17 00:00:00 2001 From: Petr Velycko Date: Mon, 19 May 2025 21:36:49 +0200 Subject: [PATCH] chybejici pt --- linearni-rovnice-konst-koef.tex | 2 +- skripta.pdf | Bin 227263 -> 227262 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/linearni-rovnice-konst-koef.tex b/linearni-rovnice-konst-koef.tex index 4b2fb64..36afb64 100644 --- a/linearni-rovnice-konst-koef.tex +++ b/linearni-rovnice-konst-koef.tex @@ -72,7 +72,7 @@ Z obecného tvaru řešení dostáváme, že $x(t) = \Phi(t) \Phi^{-1}(t_0) x_0$ Další otázka, kterou se budeme zabývat, je hledání maticové exponenciály. K tomu použijeme takzvaný Jordanův kanonický tvar matice. \begin{theorem} - Nechť $A \in \R^{n \times n}$, $J$ její Jordanův kanonický tvar, $A = VJV^{-1}$ a $(\lambda_1, \dots, \lambda_n)$ je diagonála $J$. Potom $e^{tA} = Ve^{tJ}V^{-1}$, kde matici $e^{tJ}$ definujeme jako $diag(e^{t\lambda_1}, \dots, e^{t\lambda_n})$, přičemž $P(t)$ je blokově diagonální matice se stejně velkými a stejně uspořádanými bloky jako $J$ a blok velikosti $k$ matice $P(t)$ je roven + Nechť $A \in \R^{n \times n}$, $J$ její Jordanův kanonický tvar, $A = VJV^{-1}$ a $(\lambda_1, \dots, \lambda_n)$ je diagonála $J$. Potom $e^{tA} = Ve^{tJ}V^{-1}$, kde matici $e^{tJ}$ definujeme jako $diag(e^{t\lambda_1}, \dots, e^{t\lambda_n})P(t)$, přičemž $P(t)$ je blokově diagonální matice se stejně velkými a stejně uspořádanými bloky jako $J$ a blok velikosti $k$ matice $P(t)$ je roven $$ \begin{pmatrix} 1 & t & \frac{1}{2}t^2 & \cdots & \frac{1}{(k-1)!}t^{k-1} \\ 0 & 1 & t & \cdots & \frac{1}{(k-2)!}t^{k-2} \\ diff --git a/skripta.pdf b/skripta.pdf index ec31b1079b5a3f4a56f4253ce2c0417b98bcd966..4ec16d4160a063e53f0b00fb2e4640fa7dec0cbf 100644 GIT binary patch delta 13122 zcmai)Q*59Ou!gs`ZQHhOyIb4lwqI@A?bf!r_13nww(awuyK{Gvxtz%)lgYfvGjHED zLhm&~Kr;v<62KuS2$QFHQj2hYP+@g9B5WQ*xy&=7I&&u!nH(XLUb zW!{%-I}kqO|L6O2W4EmivG1z~8R}y^KqXwOESO^w7D%{rV*gXEB1vc<@Uen$e3Rzt zJk#NV5AO7P_)uH_<2HwHx?}iTjWRAIoIfaU78>SdYyt0359~qV3rqS9QAo+T zyK`cvG8M=x?R!hPmO|_sf#YwZlZWF z#+Td2DDErbg{@4F=A>HDd%sNzA+L81992jIKB<0UbOJZ{-9TyXD%b4Zxd60mH@PbtC!q%d!~T$ez- zOyCB0QiPSPnces#|6X|uK|&YoaK5(IU|;iy7y*o#@|qY7Pk9La$JO2Hq%Rt_V;FjL 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