Talk:Eigenvalue - Revision history

FrankC: /* Question about real vs. complex spaces */

2010-05-05T13:04:46Z

Question about real vs. complex spaces

FrankC: /* Question about real vs. complex spaces */

2010-05-05T12:50:33Z

Question about real vs. complex spaces

FrankC: /* Question about real vs. complex spaces */

2010-05-04T13:48:26Z

Question about real vs. complex spaces

JacobB at 19:35, May 2, 2010

2010-05-02T19:35:15Z

FrankC: /* Question about real vs. complex spaces */

2010-05-02T19:17:43Z

Question about real vs. complex spaces

FrankC: sp

2010-05-02T19:14:32Z

FrankC: /* Question about real vs. comples spaces */

2010-05-02T19:05:58Z

Question about real vs. comples spaces

JacobB at 19:04, May 2, 2010

2010-05-02T19:04:15Z

FrankC: Created page with '== Question about real vs. comples spaces == In the definition, only ''real'' spaces are taken into account. So it doesn't make sense to speak of a ''complex'' eigenvalue, as fo…'

2010-05-02T18:54:48Z

Created page with '== Question about real vs. comples spaces == In the definition, only ''real'' spaces are taken into account. So it doesn't make sense to speak of a ''complex'' eigenvalue, as fo…'

New page

== Question about real vs. comples spaces ==

In the definition, only ''real'' spaces are taken into account. So it doesn't make sense to speak of a ''complex'' eigenvalue, as for real matrices and real vectors the equation

:<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>

cannot be solved for a non-real λ (on the left hand side, there will always be a real vector!): only the real roots of the characteristic polynom are eigenvalues!

[[User:FrankC|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)

@@ Line 28: / Line 28: @@
 ::::*''If the characteristic polynom splits into linear factors, then the determinant equals the product of the eigenvalues to the power of their algebraic multiplicity''
 ::::Thanks, [[User:FrankC|FrankC aka ComedyFan]] 09:48, 4 May 2010 (EDT)
-:::::Well, I [[determinant|changed]] it myself... [[User:FrankC|FrankC aka ComedyFan]] 08:50, 5 May 2010 (EDT)
+:::::Well, I [[determinant|changed]] it myself (see [[talk:determinant]] for details) ... [[User:FrankC|FrankC aka ComedyFan]] 08:50, 5 May 2010 (EDT)

← Older revision		Revision as of 12:50, May 5, 2010
Line 28:		Line 28:
	::::*''If the characteristic polynom splits into linear factors, then the determinant equals the product of the eigenvalues to the power of their algebraic multiplicity''		::::*''If the characteristic polynom splits into linear factors, then the determinant equals the product of the eigenvalues to the power of their algebraic multiplicity''
	::::Thanks, [[User:FrankC\|FrankC aka ComedyFan]] 09:48, 4 May 2010 (EDT)		::::Thanks, [[User:FrankC\|FrankC aka ComedyFan]] 09:48, 4 May 2010 (EDT)
		+	:::::Well, I [[determinant\|changed]] it myself... [[User:FrankC\|FrankC aka ComedyFan]] 08:50, 5 May 2010 (EDT)

← Older revision		Revision as of 13:48, May 4, 2010
Line 23:		Line 23:
	:::The issue, Frank, is that the definition is not only for real spaces - eigenvalues are a property of a linear transformation, which can be performed on any vector space, real, complex, or anything else. If you know anything about this subject, then you're obviously troublemaking, and if you don't, then your edit patterns since returning from your three month block indiciates an attempt to add nonsense.		:::The issue, Frank, is that the definition is not only for real spaces - eigenvalues are a property of a linear transformation, which can be performed on any vector space, real, complex, or anything else. If you know anything about this subject, then you're obviously troublemaking, and if you don't, then your edit patterns since returning from your three month block indiciates an attempt to add nonsense.
	:::Frankly, Frank, when a user is blocked for three months a pretty clear message has been sent. Now, obviously, we believe there may still be hope for that editor, or they would have been banned eternally, but don't go around starting stupid fights immediately. I recommend you stay away from math articles - I watch them closely. [[User:JacobB\|JacobB]] 15:35, 2 May 2010 (EDT)		:::Frankly, Frank, when a user is blocked for three months a pretty clear message has been sent. Now, obviously, we believe there may still be hope for that editor, or they would have been banned eternally, but don't go around starting stupid fights immediately. I recommend you stay away from math articles - I watch them closely. [[User:JacobB\|JacobB]] 15:35, 2 May 2010 (EDT)
		+	::::Okay, but could you please change the [[determinant\|phrase]]
		+	::::*'' The determinant is equal to the product of the eigenvalues of a matrix.''
		+	::::into something more correct, like
		+	::::*''If the characteristic polynom splits into linear factors, then the determinant equals the product of the eigenvalues to the power of their algebraic multiplicity''
		+	::::Thanks, [[User:FrankC\|FrankC aka ComedyFan]] 09:48, 4 May 2010 (EDT)

← Older revision		Revision as of 19:35, May 2, 2010
Line 21:		Line 21:

	::[[User:FrankC\|FrankC aka ComedyFan]] 15:17, 2 May 2010 (EDT)		::[[User:FrankC\|FrankC aka ComedyFan]] 15:17, 2 May 2010 (EDT)
		+	:::The issue, Frank, is that the definition is not only for real spaces - eigenvalues are a property of a linear transformation, which can be performed on any vector space, real, complex, or anything else. If you know anything about this subject, then you're obviously troublemaking, and if you don't, then your edit patterns since returning from your three month block indiciates an attempt to add nonsense.
		+	:::Frankly, Frank, when a user is blocked for three months a pretty clear message has been sent. Now, obviously, we believe there may still be hope for that editor, or they would have been banned eternally, but don't go around starting stupid fights immediately. I recommend you stay away from math articles - I watch them closely. [[User:JacobB\|JacobB]] 15:35, 2 May 2010 (EDT)

← Older revision		Revision as of 19:17, May 2, 2010
Line 11:		Line 11:

	::So please, enlighten me. [[User:FrankC\|FrankC aka ComedyFan]] 15:05, 2 May 2010 (EDT)		::So please, enlighten me. [[User:FrankC\|FrankC aka ComedyFan]] 15:05, 2 May 2010 (EDT)
		+	::What are the eigenvalues of the ''real'' matrix
		+
		+	::<math>\begin{pmatrix}
		+	0 & 1 \\
		+	-1 & 0
		+	\end{pmatrix}</math>.
		+
		+	::There aren't any! Of course, you can cheat and embed it in a complex space, but that's a different animal altogether!
		+
		+	::[[User:FrankC\|FrankC aka ComedyFan]] 15:17, 2 May 2010 (EDT)

← Older revision		Revision as of 19:14, May 2, 2010
Line 1:		Line 1:
−	== Question about real vs. ~~comples~~ spaces ==	+	== Question about real vs. complex spaces ==

	In the definition, only ''real'' spaces are taken into account. So it doesn't make sense to speak of a ''complex'' eigenvalue, as for real matrices and real vectors the equation		In the definition, only ''real'' spaces are taken into account. So it doesn't make sense to speak of a ''complex'' eigenvalue, as for real matrices and real vectors the equation

← Older revision		Revision as of 19:05, May 2, 2010
Line 8:		Line 8:

	[[User:FrankC\|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)		[[User:FrankC\|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)
−	:Oh, ''you're'' back. I don't think you know what you're talking about on this one. [[User:JacobB\|JacobB]] 15:04, 2 May 2010 (EDT)	+	:Oh, ''you're'' back. I don't think you know what you're talking about on this one. [[User:JacobB\|JacobB]] 15:04, 2 May 2010 (EDT
		+
		+	::So please, enlighten me. [[User:FrankC\|FrankC aka ComedyFan]] 15:05, 2 May 2010 (EDT)

← Older revision		Revision as of 19:04, May 2, 2010
Line 8:		Line 8:

	[[User:FrankC\|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)		[[User:FrankC\|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)
		+	:Oh, ''you're'' back. I don't think you know what you're talking about on this one. [[User:JacobB\|JacobB]] 15:04, 2 May 2010 (EDT)