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Some questions about linear transformation

  1. May 9, 2005 #1

    Eus

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    Hi Ho! ^^v

    I've some questions regarding linear transformation in my linear algebra course, guys!
    Please help me! ^^v

    Statement: A linear transformation is a special type of function.

    My answer: Yes, it is a special type of function because it must satisfy the following properties from the definition of linear transformations which is
    A transformation (or mapping) T is linear if:
    1. T(c u + d v) = c T(u) + d T(v) for all u, v in the domain of T;
    2. T(c u) = c T(u) for all u and all scalars c.

    Am I right?

    Statement: The superposition principle is a physical description of a linear transformation.
    Note: In my book it is written, I rephrased it, the superposition principle is defined as the generalization of the definition of linear transformation (i.e. T(c1 v1 + ... + cp vp) = c1 T(v1) + ... + cp T(vp) for v1...vp in the domain of T and c1...cp are scalars)

    My answer: Yes, it is because a physical event can be determined to be linear if the "input" conditions can be expressed as a linear combination of such "input" and the system's response is the same linear combination of the responses to the indiviual "input".

    Am I right?

    Maybe you could provide me with a better answer, please? ^^

    Thank you very much, guys!
    Any help would be appreciated! ^^v
     
  2. jcsd
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