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What Is linear algebra like?

  1. Jan 14, 2006 #1
    HI, I am taking linear algebra this semester, So i wanted to know..what does linear algebra deals with? Is it really hard? Can sonme one shed some light?
     
  2. jcsd
  3. Jan 14, 2006 #2

    matt grime

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    The hadnwavy stuff:

    It deals with potentially any aspect of maths that is algebraic, so involves operations of addition and multiplication, and such that these operations are linear. Something earns the title linear if it has to do with lines, planes and so on. Such things can be given by equations that are linear in the sense of they only involve x,y etc and NOT x^2, y^2 or higher powers.

    It is a vast subject, and it is very easy to learn, hard to describe because there is so much of it. I suspect your course will deal with:

    vectors, vector spaces, linear maps (matrices), solving linear equations in more than one unknown. It might go on to talk about determinants, eigenvectors, eigenspaces.

    It is practical, and has a very elegant theoretical aspect as well, but above all what you're going to do with it is most definitely not difficult.
     
  4. Jan 14, 2006 #3
    Good definition!

    Here is mine

    Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry. ...
    May sound complicated, not really though...
     
  5. Jan 14, 2006 #4

    matt grime

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    for me the reference to functional analysis and analytic geometry is unnecessary, confusing, and overly complicated. who is going to even need to know what analytic geometry is?
     
  6. Jan 14, 2006 #5
    Linear Algebra

    Hello,
    Linear Algebra is indispensible for the study of the most topics in physical, biological, social, and natural sciences. For examples It deals with systems of linear equations and matrices. Determinats, Vector space, Real inner product space Linear transformations, Eginvalues, Eginvactors, and Quadratic forms. There are more about matrix and decompositions in higher rank, but in the elementary Linear Algebra you are dealing with previuos subject.
    Best regards, Kouros
     
  7. Jan 14, 2006 #6
    In english that would mean
    y=x+c
    or
    y=ax^2+bx+c
    ...kind of equations... So dont be discouraged by the words used in the various definitions given.
     
  8. Jan 14, 2006 #7

    mathwonk

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    linear algebra is like oatmeal, not much to it, but it will never let you down, and is frequently useful.


    actually there is no such thing as linear algebra but there is such a thing as a linear differential operator. i.e. learn about linear differential equations and you will understand linear algebra.:tongue:
     
  9. Jan 14, 2006 #8

    mathwonk

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  10. Jan 14, 2006 #9
    This is not Linear Algebra You are talking about


    NOTICED !!!!!

    Hello
    what are you talking about is Algebra not Linear Algebara.
     
  11. Jan 14, 2006 #10
    As I define that the subject of linear Algebra are:
    It deals with systems of linear equations and matrices. Determinats, Vector space, Real inner product space Linear transformations, Eginvalues, Eginvactors, and Quadratic forms. There are more about matrix and decompositions in higher rank, but in the elementary Linear Algebra you are dealing with previuos subject.
     
  12. Jan 14, 2006 #11
    Hello these equation
    What are you writing for example: y=x+c y=ax^2+bx+c is belong to subject of Algebra.
    Regards
    Kouros
     
  13. Jan 14, 2006 #12
    No differential equations is other subject of mathematics. As I have studied both of that, it is simply deals with vectors and vector spaces. It is not really difficult subject, it is very useful and there are a lot of applications where you can use that.
     
  14. Jan 14, 2006 #13
    Matt Grime, you are right and that definition is perfect.
     
  15. Jan 14, 2006 #14
    coordinate geometry

    The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry is also called coordinate geometry since the objects are described as -tuples of points (where in the plane and 3 in space) in some coordinate system.
     
  16. Jan 14, 2006 #15
    Can someone define what is Moduli of elasticity ?
     
  17. Jan 14, 2006 #16
    i've just finished my course in linear algebra. and at my university, it wasn't just boring (to me anyway) but it was a giant waste of time. unfortunately, we covered more complex linear algebra material in our calculus course than in the actual LA course.

    linear algebra is good for a backbone, deals with vectors and matrices plenty which become very useful in physics. I tried to do algebra instead but they insist on physicists here taking the LA course instead which seems to be about a third of the intensity, anyone know why that might be? i guessed they might want to introduce kinds of math in physics itself but I think i'd have preferred to boost my math knowledge as high as possible.

    my LA course was easy with a bit of work, subjective of course but meh, you'll be fine.
     
  18. Jan 14, 2006 #17
    It is very useful subject you use that for all your scientific field in computer science programming and all Engineering and sciences. There are 2 kinds of course in my University one is Linear Algebra, and other is higher rank called Matrix. Which deal with LU decompositions.
     
  19. Jan 14, 2006 #18
    Can someone define what is Moduli of elasticity ?

    The modoli of elasticity Elastic compliance and stifness constants. For example Hook's law state that for small deformations the strain is proportional to the stress, so that strain components are linear functions of the stress components.
    Cxx=s11Xx+S12 Yy+s13+s14Yz+s15Zx+S16Xy;
    Cyy=s21Xx+S22 Yy+s23+s24Yz+s25Zx+S26Xy;
    Czz=........................................................;
    Cyz=.......................................................;
    Czx=.......................................................;
    Cxy=.......................................................;
     
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