From b6d669ebc15cafdbab0e79e875074468bcec7779 Mon Sep 17 00:00:00 2001
From: Holden Rohrer <hr@hrhr.dev>
Date: Tue, 14 Apr 2020 13:54:12 -0400
Subject: fixed another matrix rep error

---
 execsumm/document.tex | 23 +++++++++++------------
 1 file changed, 11 insertions(+), 12 deletions(-)

diff --git a/execsumm/document.tex b/execsumm/document.tex
index 8ed5e21..f3cf093 100644
--- a/execsumm/document.tex
+++ b/execsumm/document.tex
@@ -12,22 +12,21 @@ is useful (this form was chosen to reduce fractions' usage):
 $$\x' =
 {1\over R_1C_1C_2\rload}
 \pmatrix{0&-C_2\rload      &0 \cr
-         0&-C_2(R_1+\rload)&-C_1\rload\cr
-         0&C_2R_1          &-C_1\rload}   \x +
+         0&-C_2(R_1+\rload)&-C_1R_1\cr
+         0&C_2R_1          &-C_1R_1}   \x +
 {1\over R_1}
 \pmatrix{\omega\cos(\omega t)\cr
          \omega\cos(\omega t)\cr
          0}
-.
-$$
+.$$
 The characteristic polynomial is
-$$-\lambda( (-\lambda-C_2(R_1+\rload))(-\lambda-C_1\rload)
-+ C_2C_1R_1\rload).$$
+$$-\lambda( (-\lambda-C_2(R_1+\rload))(-\lambda-C_1R_1)
++ C_2C_1R_1^2).$$
 Expanded,
-$$-\lambda( \lambda^2 + \lambda(C_2(R_1+\rload)+C_1\rload)
-+ C_1C_2\rload(2R_1+\rload)).$$
-In terms of its roots (with $b=C_2(R_1+\rload)+C_1\rload$ and
-$c = C_1C_2\rload(2R_1+\rload),$
+$$-\lambda( \lambda^2 + \lambda(C_2(R_1+\rload)+C_1R_1)
++ C_1C_2R_1(2R_1+\rload)).$$
+In terms of its roots (with $b=C_2(R_1+\rload)+C_1R_1$ and
+$c = C_1C_2R_1(2R_1+\rload),$
 $$-\lambda{(\lambda-{-b+\sqrt{b^2-4c}\over2})
 (\lambda-{-b-\sqrt{b^2-4c}\over 2})}$$
 %For reference,
@@ -40,9 +39,9 @@ Let $r_1$ and $r_2$ designate these two non-zero roots.
 
 \bu $\lambda_1 = 0, v_1 = \pmatrix{1\cr0\cr0}$
 
-\bu $\lambda_2 = r_1, v_2 = ??$
+\bu $\lambda_2 = {r_1\over C_1C_2R_1\rload}, v_2 = ??$
 
-\bu $\lambda_3 = r_2, v_3 = ??$
+\bu $\lambda_3 = {r_2\over C_1C_2R_1\rload}, v_3 = ??$
 
 \section{Nonhomogenous System}
 
-- 
cgit