Results 1 to 3 of 3

Math Help - Theoretical Question

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    3

    Theoretical Question

    We have a real 2x2 matrix A with 2 distinct real eigenvalues, lambda1 and lambda 2. explain the formula detA = lambda1(lambda 2) geometrically, thinking of module(detA) as an explansion facor. illustrate your explanation with a sketch. can you explain this similarly for 3x3 matrices?

    i dont even know where to begin! and thanks for the help in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by satweety12 View Post
    We have a real 2x2 matrix A with 2 distinct real eigenvalues, lambda1 and lambda 2. explain the formula detA = lambda1(lambda 2) geometrically, thinking of module(detA) as an explansion facor. illustrate your explanation with a sketch. can you explain this similarly for 3x3 matrices?

    i dont even know where to begin! and thanks for the help in advance!

    I'm not completely sure whether the question is clear enough to me, but I can think of the following: if the matrix A has two eigenvalues \lambda_1\neq \lambda_2, then A is similar to the matrix A'=\left(\begin{array}{cc}\lambda_1&0\\0&\lambda_2  \end{array}\right) , and since we know that \det A=\det A' , and this last one has a very nice and simple geometric interpretation we get (?) what we want: it is the "volume" (generalized algebraic volume, which in this case is 2-dimensional volume = usual area) of the parallelogram (rectangle in this case) generated by the 2-dimensional vectors (\lambda_1\,\;0)\,,\;(0\,,\;\lambda_2)\,\;in\,\;\m  athbb{R}^2

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    3

    thanks!

    thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. theoretical question on cyclic function
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 22nd 2010, 01:01 AM
  2. theoretical question on solutions..
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 21st 2010, 11:43 PM
  3. Help With Theoretical MAtrices Question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 6th 2009, 12:33 PM
  4. Basis (theoretical question)
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 25th 2009, 07:26 AM
  5. Theoretical question on infinity and limit
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 18th 2009, 04:35 PM

Search Tags


/mathhelpforum @mathhelpforum