From 15bfb7730801809704c6561e20c5ca47627b2d79 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 21 Feb 2021 20:53:46 +0100
Subject: Add "Gram-Schmidt method"

---
 latex/know/concept/partial-fraction-decomposition/source.md | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

(limited to 'latex/know/concept/partial-fraction-decomposition')

diff --git a/latex/know/concept/partial-fraction-decomposition/source.md b/latex/know/concept/partial-fraction-decomposition/source.md
index aa03f9c..69428e7 100644
--- a/latex/know/concept/partial-fraction-decomposition/source.md
+++ b/latex/know/concept/partial-fraction-decomposition/source.md
@@ -3,7 +3,7 @@
 
 # Partial fraction decomposition
 
-*Partial fraction decomposition* or *expansion* is a method to rewrite a
+**Partial fraction decomposition** or **expansion** is a method to rewrite a
 quotient of two polynomials $g(x)$ and $h(x)$, where the numerator
 $g(x)$ is of lower order than $h(x)$, as a sum of fractions with $x$ in
 the denominator:
@@ -21,9 +21,9 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Then the constant coefficients $c_n$ can either be found the hard way,
+The constants $c_n$ can either be found the hard way,
 by multiplying the denominators around and solving a system of $N$
-equations, or the easy way by using the following trick:
+equations, or the easy way by using this trick:
 
 $$\begin{aligned}
     \boxed{
@@ -31,8 +31,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-If $h_1$ is a root with multiplicity $m > 1$, then the sum takes the
-form of:
+If $h_1$ is a root with multiplicity $m > 1$, then the sum takes the form of:
 
 $$\begin{aligned}
     \boxed{
@@ -41,8 +40,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where $c_{1,j}$ are found by putting the terms on a common denominator,
-e.g.:
+Where $c_{1,j}$ are found by putting the terms on a common denominator, e.g.
 
 $$\begin{aligned}
     \frac{c_{1,1}}{x - h_1} + \frac{c_{1,2}}{(x - h_1)^2}
-- 
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