Matrix function problem

Thread Starter

FBorges22

Joined Sep 11, 2008
109
Well... basically I have to calculate the eigenvalues and eigenvectors manually because I need to present the solution of the problem to the my professor...

In the eigeinvector calculator I misplaced the number 0 with 2... ooopss..XD

The E matrix is in this format?

\(
E = \[ \begin{array}{ccc}
\lambda_{1} & 0 & 0 \\
0 & \lambda_{2} & 0 \\
0 & 0 & \lambda_{3} \end{array}
\]
\)
 

Thread Starter

FBorges22

Joined Sep 11, 2008
109
Well... let's try.. The answer to my question is?

\(
cos(\pi*A/4) = \[ \begin{array}{ccc}
1 & 1 & 1 \\
-1 & -2 & 1 \\
1 & 4 & 1 \end{array}
\]*\[ \begin{array}{ccc}
-cos(\pi/4) & 0 & 0 \\
0 & -2cos(\pi/4) & 0 \\
0 & 0 & cos(\pi/4) \end{array}
\]*\[ \begin{array}{ccc}
1 & -1/2 & -1/2 \\
-1/3 & 0 & 1/3 \\
1/3 & 1/2 & 1/6 \end{array}
\]

\)
 

Thread Starter

FBorges22

Joined Sep 11, 2008
109
I tried to multiply in my HP 50g calculator and he gave a strange results... Could check for me in the matlab, please? I am at a cybercafe right now and I am far from home without access... XD

When I return I will try too... and then we can compare our results

Thanks
 
Upon closer examination, it should be:
\(
cos(\pi*A/4) = \[ \begin{array}{ccc}
1 & 1 & 1 \\
-1 & -2 & 1 \\
1 & 4 & 1 \end{array}
\]*\[ \begin{array}{ccc}
cos(-\pi/4) & 0 & 0 \\
0 & cos(-2\pi/4) & 0 \\
0 & 0 & cos(\pi/4) \end{array}
\]*\[ \begin{array}{ccc}
1 & -1/2 & -1/2 \\
-1/3 & 0 & 1/3 \\
1/3 & 1/2 & 1/6 \end{array}
\]

\)

I did it on an HP50g. Make sure you're in exact mode, and you may have to simplify your result. I got the same result as in post #4.
 

t_n_k

Joined Mar 6, 2009
5,455
I use Scilab, which includes the matrix cosine function 'cosm(X)' where X is the given matrix. It returns the same values as shown in Electricians's post #4 - for this particular problem. I'm not sure that a similar Matlab function exists, but I would be surprised if it didn't.

This might be of interest to Georacer who had made reference to the element-by-element Matlab function cos(X), where X is a matrix. This was of course the same simple element-by-element solution I had originally suggested.

Shows how careful one has to be in offering a solution in the absence of a full disclosure of the original question.
 

Georacer

Joined Nov 25, 2009
5,182
Well, to tell the truth, I have never met an equivalent "cosm" function anywhere, and in my control systems classes the simple "cos" function is very commonly used, so I presumed it was the one required. I guess you can't be carefull enough when writing a question as well as when reading one.
 

Thread Starter

FBorges22

Joined Sep 11, 2008
109
Ok... Did on the matlab and I reached this result... Could you confirm for me please?

\(
cos(\pi*A/4) = \[ \begin{array}{ccc}
0.9428 & 0 & -0.2357 \\
-0.4714 & 0.7071 & 0.4714 \\
0.9428 & 0 & -0.2357 \end{array}
\]
\)

I am going also to solve in the HP 50g... I think this question needs to be delivered in the non-decimal form... i.e., include pi member over the fractions
 

t_n_k

Joined Mar 6, 2009
5,455
Ok... Did on the matlab and I reached this result... Could you confirm for me please?

\(
cos(\pi*A/4) = \[ \begin{array}{ccc}
0.9428 & 0 & -0.2357 \\
-0.4714 & 0.7071 & 0.4714 \\
0.9428 & 0 & -0.2357 \end{array}
\]
\)
That's what I got.

Electrician gave the exact form using whole fractions / surds in post #4.
 

Thread Starter

FBorges22

Joined Sep 11, 2008
109
Well... I guess we did it... I am going to show the results to my class and soon I will gave more news about this problem.
 
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