Math@Funny@Honey@Money

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Math@Funny@Honey@Money

أسرة الموقع ترحب بك و نتمنى أن تكون بتمام الصحة و العافيه

Math@Funny@Honey@Money

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Math@Funny@Honey@Money



    linear transformation

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    ذكر
    عدد الرسائل : 439
    العمر : 36
    Location : Egypt
    Job/hobbies : learner
    Skills/Courses : egypt
    Mood : linear transformation 7adnb6
    الأوسمة : linear transformation 68238983oi3sk3
    تاريخ التسجيل : 05/04/2008

    m14 linear transformation

    مُساهمة من طرف teacher الخميس 24 يوليو 2008, 3:06 pm


    A linear transformation between two vector spaces linear transformation Inline1 and linear transformation Inline2 is a map linear transformation Inline3 such that the following hold:
    1. linear transformation Inline4 for any vectors linear transformation Inline5 and linear transformation Inline6 in linear transformation Inline7, and
    2. linear transformation Inline8 for any scalar linear transformation Inline9.
    A linear transformation may or may not be injective or surjective. When linear transformation Inline10 and linear transformation Inline11 have the same dimension, it is possible for linear transformation Inline12 to be invertible, meaning there exists a linear transformation Inline13 such that linear transformation Inline14. It is always the case that linear transformation Inline15. Also, a linear transformation always maps lines to lines (or to zero).

    linear transformation LinearTransformation_701
    linear transformation LinearTransformation3D_700

    The main example of a linear transformation is given by matrix multiplication. Given an linear transformation Inline16 matrix linear transformation Inline17, define linear transformation Inline18, where linear transformation Inline19 is written as a column vector (with linear transformation Inline20 coordinates). For example, consider

    linear transformation NumberedEquation1(1)
    then linear transformation Inline21 is a linear transformation from linear transformation Inline22 to linear transformation Inline23, defined by,

    linear transformation NumberedEquation2(2)
    linear transformation Lineartr
    Another example is linear transformation Inline24, and the homotopy from the identity transformation to linear transformation Inline25 is illustrated above.
    When linear transformation Inline26 and linear transformation Inline27 are finite dimensional, a general linear transformation can be written as a matrix multiplication only after specifying a vector space basis for linear transformation Inline28 and linear transformation Inline29. When linear transformation Inline30 and linear transformation Inline31 have an inner product, and their vector space bases, linear transformation Inline32 and linear transformation Inline33, are orthonormal, it is easy to write the corresponding matrix linear transformation Inline34. In particular, linear transformation Inline35. Note that when using the standard basis for linear transformation Inline36 and linear transformation Inline37, the linear transformation Inline38th column corresponds to the image of the linear transformation Inline39th standard basis vector.
    When linear transformation Inline40 and linear transformation Inline41 are infinite dimensional, then it is possible for a linear transformation to not be continuous. For example, let linear transformation Inline42 be the space of polynomials in one variable, and linear transformation Inline43 be the derivative. Then linear transformation Inline44, which is not continuous because linear transformation Inline45 while linear transformation Inline46 does not converge.
    Linear two-dimensional transformations have a simple classification. Consider the two-dimensional linear transformation

    linear transformation Inline47linear transformation Inline48linear transformation Inline49(3)
    linear transformation Inline50linear transformation Inline51linear transformation Inline52(4)
    Now rescale by defining linear transformation Inline53 and linear transformation Inline54. Then the above equations become

    linear transformation NumberedEquation3(5)
    where linear transformation Inline55 and linear transformation Inline56, linear transformation Inline57, linear transformation Inline58, and linear transformation Inline59 are defined in terms of the old constants. Solving for linear transformation Inline60 gives

    linear transformation NumberedEquation4(6)
    so the transformation is one-to-one. To find the fixed points of the transformation, set linear transformation Inline61 to obtain

    linear transformation NumberedEquation5(7)
    This gives two fixed points, which may be distinct or coincident. The fixed points are classified as follows.

    lol!
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    ذكر
    عدد الرسائل : 439
    العمر : 36
    Location : Egypt
    Job/hobbies : learner
    Skills/Courses : egypt
    Mood : linear transformation 7adnb6
    الأوسمة : linear transformation 68238983oi3sk3
    تاريخ التسجيل : 05/04/2008

    m14 رد: linear transformation

    مُساهمة من طرف teacher الخميس 24 يوليو 2008, 3:07 pm



    [tr][td]variables
    [/td]
    [td] type
    [/td][/tr]
    [tr][td]linear transformation Inline62
    [/td]
    [td] hyperbolic fixed point
    [/td][/tr]

      الوقت/التاريخ الآن هو الخميس 28 مارس 2024, 1:13 pm