From 852640e19ad544c4bbb6f7c0749b2138eeb91ce7 Mon Sep 17 00:00:00 2001 From: Timothy Skipper Date: Tue, 14 Nov 2023 18:06:01 +0100 Subject: [PATCH 1/2] Fix: Typo in exercise 12E --- tex/linalg/dets.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tex/linalg/dets.tex b/tex/linalg/dets.tex index fd121244..6fb21360 100644 --- a/tex/linalg/dets.tex +++ b/tex/linalg/dets.tex @@ -518,7 +518,7 @@ \section{Characteristic polynomials, and Cayley-Hamilton} \gim A herd of $1000$ cows of nonzero weight is given. Prove that we can remove one cow such that the remaining $999$ cows - cannot be partition into two sets with equal sum of weights. + cannot be partitioned into two sets with equal sum of weights. \begin{hint} Consider $1000 \times 1000$ matrix $M$ with entries $0$ on diagonal and $\pm 1$ off-diagonal. From 44995af21f77c817630b0d68c85c414116a2f26d Mon Sep 17 00:00:00 2001 From: Timothy Skipper Date: Tue, 14 Nov 2023 20:05:19 +0100 Subject: [PATCH 2/2] Fix: Typo in Hilbert Spaces --- tex/linalg/inner-form.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tex/linalg/inner-form.tex b/tex/linalg/inner-form.tex index aa69e9e3..cf306e17 100644 --- a/tex/linalg/inner-form.tex +++ b/tex/linalg/inner-form.tex @@ -360,7 +360,7 @@ \section{Hilbert spaces} Here is how it goes: \begin{definition} - A \vocab{Hilbert space} is a inner product space $V$, + A \vocab{Hilbert space} is an inner product space $V$, such that the corresponding metric space is complete. \end{definition}