ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 14 Oct 2015 09:11:18 +0200eigenvectors of complex matrixhttps://ask.sagemath.org/question/29989/eigenvectors-of-complex-matrix/Hi!
I would like to find the complex eigenvectors of this matrix:
A=matrix(CDF,[[2-i,0,i],[0,1+i,0],[i,0,2-i]]).
I have used the command A.eigenvectors_right() and I get the following eigenvectors (rounded off):
(-0.70711+9.4136e-17i , 0 , 0.70711), (0,1,0), (0.70711 , 0 , 0.70711)
In my checklist I should get the vectors: t1*(-1,0,1), t2*(0,1,0), t3*(1,0,1), where the t-values are complex factors.
How do I compute this kind of result?
Sincerly SimonismonWed, 14 Oct 2015 09:11:18 +0200https://ask.sagemath.org/question/29989/Working with complex symbolic expressionshttps://ask.sagemath.org/question/8716/working-with-complex-symbolic-expressions/I am a beginner at Sage so my questions may not be well informed, so bear with me.
The context: I am trying to use sage to explore the exponential function assuming all I know about it is that it is its own derivative and has the value 1 at z = 0. It is then easy to develop the Taylor series to any degree using formula like:
expp2( z ) = 1 + ( 1/ factorial( 1 ) )* z + ( 1/ factorial( 2 ) ) * ( z ^ 2 )
You can take 2 of these for z = a and z = b and multiply them together in Sage. Getting something like:
1/4*(b^2 + 2*b + 2)*(a^2 + 2*a + 2)
Now I have done the algebra by hand and know this reduces to the Taylor expansion for z = a + b.
What I do not get is how to show this part in Sage in a nice clean way ( I have some ways I do not like so much ).
Here I have 2 questions one specific, and one general ( I am interested in the answer to either one or both):
1) If this exponential question interests anyone, could you offer some tips? I have tried various ( but not all ) applications of expand and simplify. I am still plugging away.
2) Is there a guide that would help me learn how to carry out algebraic operations over complex expressions. I have looked at several basic tutorials, but they do not have much detail. The most useful single resource I have found is
http://www.sagemath.org/doc/reference/sage/symbolic/expression.html
and the pages linking from it.
russ_henselMon, 13 Feb 2012 15:07:47 +0100https://ask.sagemath.org/question/8716/