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Confusing about linearity and nonlinearity

  1. Aug 22, 2009 #1

    KFC

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    Hi there, in the course of linear algebra, we talk about many on matrix and related properities. I wonder if any equations written in terms of matrices are linear? Could nonlinear equations also written in matrices?

    Thanks
     
  2. jcsd
  3. Aug 22, 2009 #2
    Suppose [itex]A[/itex] is an [itex]n \times n[/itex] matrix and [itex]\mathbf{x}[/itex] is [itex]n \times 1[/itex]. Then: [itex]\mathbf{x}^{T} A \mathbf{x}[/itex] is a quadratic form in [itex]\mathbf{x}[/itex]
     
  4. Aug 22, 2009 #3
    Take any function, and express it as a taylor series. Replace x with Ax and you got a non linear function expressed in terms of matrices.
     
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