Math 260, Spring 2012 - Revision history

Steven.Jackson: Reverted edits by 31.184.238.9 (Talk) to last revision by Steven Glenn Jackson

2012-05-04T14:26:01Z

Reverted edits by 31.184.238.9 (Talk) to last revision by Steven Glenn Jackson

31.184.238.9: /* Important Dates */

2012-05-04T13:08:02Z

‎Important Dates

Steven.Jackson: Answered question on isometries

2012-04-04T12:52:03Z

Answered question on isometries

Patrick.Mclaren: Question on isometries.

2012-04-04T01:12:26Z

Question on isometries.

Steven.Jackson at 00:26, 8 March 2012

2012-03-08T00:26:43Z

Steven.Jackson: Added links to Sage.

2012-03-08T00:24:07Z

Added links to Sage.

Steven.Jackson at 15:27, 6 March 2012

2012-03-06T15:27:41Z

Patrick.Mclaren: Added a link to documentation for using matrices with Mathematica

2012-03-06T02:46:36Z

Added a link to documentation for using matrices with Mathematica

Patrick.Mclaren: Added sections and a question.

2012-03-06T02:11:11Z

Added sections and a question.

Steven.Jackson: Start page

2012-03-01T02:42:36Z

Start page

New page

'''Math 260 --- Linear Algebra I'''

Welcome to the wiki! Editing this page is exactly like editing [http://en.wikipedia.org/wiki/Main_page Wikipedia]. You may wish to see their help pages on [http://en.wikipedia.org/wiki/Help:Contents/Editing_Wikipedia editing] and on [http://en.wikipedia.org/wiki/MOS:MATH#Typesetting_of_mathematical_formulae typesetting mathematics].

(It isn't as hard as the documentation might make it seem. To see how to typeset the sentence "Consider a linear transformation <math>T:R^2\rightarrow R^2</math>," click the "edit" link at the top of this page and read the source code that generated it.)

[[User:Steven Glenn Jackson|Steven Glenn Jackson]] 02:42, 1 March 2012 (UTC)

@@ Line 7: / Line 7: @@
 [[User:Steven Glenn Jackson|Steven Glenn Jackson]] 02:42, 1 March 2012 (UTC)
+=Important Dates=
-EuJGc  <a href="http://locykgdstuhv.com/">locykgdstuhv</a>, [url=http://xfgtqmydqfna.com/]xfgtqmydqfna[/url], [link=http://yiwaczgucbyo.com/]yiwaczgucbyo[/link], http://qdafzctdlgdz.com/
+* 02/28/2012 - Exam 1
+* 04/17/2012 - Exam 2
 =Questions=

@@ Line 7: / Line 7: @@
 [[User:Steven Glenn Jackson|Steven Glenn Jackson]] 02:42, 1 March 2012 (UTC)
+EuJGc  <a href="http://locykgdstuhv.com/">locykgdstuhv</a>, [url=http://xfgtqmydqfna.com/]xfgtqmydqfna[/url], [link=http://yiwaczgucbyo.com/]yiwaczgucbyo[/link], http://qdafzctdlgdz.com/
-=Important Dates=
-* 02/28/2012 - Exam 1
-* 04/17/2012 - Exam 2
 =Questions=

@@ Line 18: / Line 18: @@
 * If <math>\varphi:\mathbb{R}^n\to\mathbb{R}^n</math> is an isometry that fixes the origin: <math>\varphi(0) = 0</math>, then does <math>\varphi</math> preserve dot products? [[User:Patrickmclaren|Patrickmclaren]] 02:12, 4 April 2012 (BST)
+: Yes.  Since <math>\phi</math> is an isometry and fixes the origin, it is linear (this is the only part that's hard to prove).  Then since it preserves distance and fixes the origin, it preserves length of vectors.  So it is an orthogonal transformation according to the book's definition.  The book gives a proof that such transformations preserve dot products.  [[User:Steven Glenn Jackson|Steven Glenn Jackson]] 13:52, 4 April 2012 (BST)
 =Links=

@@ Line 16: / Line 16: @@
 * If the kernel of a linear transformation is nontrivial, does that imply that the transformation is not injective and therefore the transformation matrix is not invertible? [[User:Patrickmclaren|Patrickmclaren]] 02:11, 6 March 2012 (GMT)
 : Yes.  If the kernel of <math>T</math> is non-trivial, then we have some non-zero <math>\vec{v}</math> with <math>T(\vec{v})=\vec{0}</math>.  But also <math>T(\vec{0})=\vec{0}</math>, so <math>T</math> is not one-to-one and hence not invertible.  [[User:Steven Glenn Jackson|Steven Glenn Jackson]] 15:27, 6 March 2012 (GMT)
+* If <math>\varphi:\mathbb{R}^n\to\mathbb{R}^n</math> is an isometry that fixes the origin: <math>\varphi(0) = 0</math>, then does <math>\varphi</math> preserve dot products? [[User:Patrickmclaren|Patrickmclaren]] 02:12, 4 April 2012 (BST)
 =Links=

@@ Line 22: / Line 22: @@
 * [http://reference.wolfram.com/mathematica/guide/MatricesAndLinearAlgebra.html Matrices and Linear Algebra in Mathematica]
 * [http://sagemath.org/ Sage], a free and open-source alternative to Mathematica and other mathematics software.  (It can either be [http://sagemath.org/download-linux.html downloaded] or used online through a [http://www.sagenb.org/ web interface].)
-* A brief guide to [[http://sagemath.org/doc/tutorial/tour_linalg.html linear algebra in Sage].  (Note that by default Sage uses row vectors and left kernels instead of column vectors and right kernels, so if you're not careful you may get into trouble with these functions.  But its reduced row echelon forms are the same as ours.)
+* A brief guide to [http://sagemath.org/doc/tutorial/tour_linalg.html linear algebra in Sage].  (Note that by default Sage uses row vectors and left kernels instead of column vectors and right kernels, so if you're not careful you may get into trouble with these functions.  But its reduced row echelon forms are the same as ours.)