Results 1 to 4 of 4

Math Help - Idempotent Matrix

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    118

    Idempotent Matrix

    I would love some guidance on how I should approach this question:

    Question: If A is an idempotent matrix of order n, show that (I+A)^n = I+(2^N-1)A
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by sparky View Post
    I would love some guidance on how I should approach this question:

    Question: If A is an idempotent matrix of order n, show that (I+A)^n = I+(2^N-1)A

    Hints:

    1) Show that \displaystyle{\sum\limits^n_{k=0}\binom{n}{k}=2^n} ;

    2) As I, A commute with each other, \displaystyle{(I+A)^n=\sum\limits^n_{k=0}A^k=I+A\s  um\limits^n_{k=1}\binom{n}{k}=} ...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    118
    Thank you for your reply Tonio.

    I am still trying to figure out how to show in your first point.

    Here is what I understand so far:

    A matrix A is said to be idempotent if A^2=A
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by sparky View Post
    Thank you for your reply Tonio.

    I am still trying to figure out how to show in your first point.

    Here is what I understand so far:

    A matrix A is said to be idempotent if A^2=A

    Well, understanding definitions is important but it's hardly enough for this problem...

    Further hint:

    Newton's Binomial Theorem: For any pair of commuting elements a,b in a ring and for

    any natural n, we have that \displaystyle{(a+b)^n=\sum\limits^n_{k=0}\binom{n}  {k}a^{n-k}b^k}

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. matrix trace and idempotent
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 15th 2010, 01:10 AM
  2. Idempotent Matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 20th 2009, 01:02 PM
  3. Idempotent matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 17th 2009, 08:52 PM
  4. Problem of Idempotent matrix
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: May 24th 2009, 06:32 AM
  5. Idempotent Matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 3rd 2008, 04:05 PM

Search Tags


/mathhelpforum @mathhelpforum