# Initial state vector

• Mar 1st 2009, 05:02 PM
thehollow89
Initial state vector
Express our initial state vector S0 as a linear combination of our eigenvectors. The initial state vector is:
_
|0|
|1|
|0|
---
This material isn't in my textbook. Any help? I appreciate all the help I've received. Just sharing. This forum rocks.
• Mar 1st 2009, 10:46 PM
CaptainBlack
Quote:

Originally Posted by thehollow89
Express our initial state vector S0 as a linear combination of our eigenvectors. The initial state vector is:
_
|0|
|1|
|0|
---
This material isn't in my textbook. Any help? I appreciate all the help I've received. Just sharing. This forum rocks.

Please provide more information, like what are your eigen vectors, or what matrix (or whatever) are they the eigen vectors of.

CB
• Mar 2nd 2009, 02:44 AM
thehollow89
Quote:

Originally Posted by CaptainBlack
Please provide more information, like what are your eigen vectors, or what matrix (or whatever) are they the eigen vectors of.

CB

Oh Sorry I didn't know how much info was needed for this part of the question. The eigenvectors are:

----
0
t ,
-t

----

,

--------
t
-5/2t
-4/9t
-------

and

------
t
1/2t
2/5t
------
• Mar 2nd 2009, 04:58 AM
HallsofIvy
You eigenvectors depend on t but your initial state vector doesn't? That's impossible. I suspect that you mean the eigenvectors are <0, 1, -1>, <1, -5/2, -4/9>, and <1, 1/2, 2/5>.

If so, then you need to find numbers a, b, c so that
a<0, 1, -1>+ b<1, -5/2, -4/9>+ c<1, 1/2, 2/5>= <0, 1, 0>

That is the same as saying <b+ c, a-(5/2)b+ (1/2)c, -a- (4/9)b+ (2/5)c>= < 0, 1, 0> or b+ c= 0, a- (5/2)b+ (1/2)c= 1, -a+ (5/9)b+ (2/5)c= 0. Solve those equations for a, b, c.
• Mar 3rd 2009, 03:17 PM
matt12321
how would i calculate another state vector from this?
like S2?
• Mar 3rd 2009, 03:19 PM
thehollow89
Quote:

Originally Posted by matt12321
how would i calculate another state vector from this?
like S2?

I take it you go to Mcmaster too? I'm trying to figure it out.
• Mar 3rd 2009, 03:21 PM
matt12321
Quote:

Originally Posted by thehollow89
I take it you go to Mcmaster too? I'm trying to figure it out.

ya,
this assignment is going to take me forever...
well actually, theres only three more real questions after this one.
• Mar 3rd 2009, 03:23 PM
thehollow89
Quote:

Originally Posted by matt12321
ya,
this assignment is going to take me forever...
well actually, theres only three more real questions after this one.

Yeah, are you using maple or online matrix multipliers? I'll be going to the help center tomorrow around 5:30-8:30 tomorrow if you wanna...well...cheat lol. Mclean doesn't even care if we cheat lol.
• Mar 3rd 2009, 03:44 PM
matt12321
i'm using online multipliers...
i used this other site to calculate the eigenvalues/vectors
but i did it by hand aswell..

i might be there tomorrow, but i'm not sure..
i'm supposed to be going somewhere tomorrow evening..
• Mar 3rd 2009, 03:45 PM
thehollow89
Alright cool.
• Mar 3rd 2009, 04:51 PM
matt12321
well i'm almost done now... i think i've done all i can do without more help...
have you done #7?
seems really dumb to me..
i haven't done the second part of number three...
and can't finish 9 because i don't have the final answer for 5 (the one above)
have you figured any of these out?
• Mar 5th 2009, 12:30 PM
a_n
i go to mcmaster too...im just wondering how to do question 6 because i really dont understand what its asking