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- #1

#### chickenwin

##### New member

- Feb 13, 2014

- 12

construct a matrix A that belongs to Mat_n*n (F) such that

V is not equal to C_x for every x that belongs to V

here,

C_x = span {x, L(x), L^2(x), .............L^k(x),.......}

- Thread starter chickenwin
- Start date

- Thread starter
- #1

- Feb 13, 2014

- 12

construct a matrix A that belongs to Mat_n*n (F) such that

V is not equal to C_x for every x that belongs to V

here,

C_x = span {x, L(x), L^2(x), .............L^k(x),.......}

- Feb 15, 2012

- 1,967

- Thread starter
- #3

- Feb 13, 2014

- 12

I do not know

I cannot figure out how A correlated to C_x. Could you please explain that to me? Thanks a ton. (heart)

- Feb 15, 2012

- 1,967

Suppose $A$ is such that $Ax = 0$ for some non-zero $x$. What can you say about $C_x$ then?

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- #5

- Feb 13, 2014

- 12

still dunno. i think i just do not get what A is with respect to C_x. i know C_x is cyclic subspace generated by x that is spanned by vectors, x, L(x),...........Suppose $A$ is such that $Ax = 0$ for some non-zero $x$. What can you say about $C_x$ then?

but what is A? how does it relate to x, L(x), C_x, etc?

- Feb 15, 2012

- 1,967

$C_x = \{x,Ax,A^2x,\dots\} = \{x,0,0,\dots\}$

HOW CAN THIS SPAN $V$?