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I think so, thanks. My maths skills are generally very poor indeed, but OTOH I have an MSc in Computer Science* so I should understand some of this sort of stuf

by user24 14y ago

I think so, thanks. My maths skills are generally very poor indeed, but OTOH I have an MSc in Computer Science* so I should understand some of this sort of stuff. I always feel like I'm missing detail, eg: > every complex linear transformation Is that "complex" important? > line that gets mapped to itself So a trivial example might be a 360 degree rotation? Or am I just way misunderstanding this stuff? * and I do mean real CS, not software engineering.

btilly 14y ago
Complex is important. The eigenvectors for rotation by 90 degrees require complex numbers.
- user24 14y ago
  I have no idea what a complex number is. I wish I'd paid more attention in school.
  - btilly 14y ago
    Complex numbers are just numbers that can have an imaginary component. Like 5+3i. All real numbers are complex (they just have an imaginary component of 0), but the converse is obviously not true.
    - user24 14y ago
      I've bookmarked the wiki page on this stuff for later. Otherwise my next question would just be "what's an imaginary component?" I don't think my tutors at Oxford really understood exactly what I meant by "I can't do all this maths". Basic gaps in my knowledge. Still passed though, fuck yeah! :D
      - lmkg 14y ago
        "Imaginary" numbers are the square roots of negative numbers. Because (-1)^2 = 1^2 = 1, these numbers don't exist on the regular ("real") number line. Instead we wave our hands and posit the existence of the magical number i, the imaginary unit, that has the property i^2 = -1. Through simple algebra, this unit is enough to give us square roots for all the imaginary numbers. For example, (3i)^2 = -9. Imaginary numbers are "independent" of the real numbers, which means that the sum of 5 and 3i is simply 5+3i. That expression cannot be simplified further. Such sums are called "complex" numbers. The complex numbers can be imagined as a plane, with the horizontal axis consisting of the pure reals, and the vertical axis consisting of the pure imaginaries. Complex numbers support all the regular arithmetic operations. You can figure them out yourself, so long as you remember i^2 = -1. In the complex plane, addition looks like vector addition, and multiplying by an imaginary number is a rotation.
ColinWright 14y ago
>> line that gets mapped to itself > So a trivial example might be a > 360 degree rotation? That's a very trivial example, and therefore good. Less trivial examples are a sheer, an expansion, or a rotation in 3D space. A rotation in 2D space apparently only leaves the origin fixed, and that's where we need complex numbers. To find a fixed line in that case we need to find roots of a quadratic with negative discriminant, hence needing sqrts of negative numbers.

by user24 14y ago

btilly 14y ago

Complex is important. The eigenvectors for rotation by 90 degrees require complex numbers.

user24 14y ago
I have no idea what a complex number is. I wish I'd paid more attention in school.
- btilly 14y ago
  Complex numbers are just numbers that can have an imaginary component. Like 5+3i. All real numbers are complex (they just have an imaginary component of 0), but the converse is obviously not true.
  - user24 14y ago
    I've bookmarked the wiki page on this stuff for later. Otherwise my next question would just be "what's an imaginary component?" I don't think my tutors at Oxford really understood exactly what I meant by "I can't do all this maths". Basic gaps in my knowledge. Still passed though, fuck yeah! :D
    - lmkg 14y ago
      "Imaginary" numbers are the square roots of negative numbers. Because (-1)^2 = 1^2 = 1, these numbers don't exist on the regular ("real") number line. Instead we wave our hands and posit the existence of the magical number i, the imaginary unit, that has the property i^2 = -1. Through simple algebra, this unit is enough to give us square roots for all the imaginary numbers. For example, (3i)^2 = -9. Imaginary numbers are "independent" of the real numbers, which means that the sum of 5 and 3i is simply 5+3i. That expression cannot be simplified further. Such sums are called "complex" numbers. The complex numbers can be imagined as a plane, with the horizontal axis consisting of the pure reals, and the vertical axis consisting of the pure imaginaries. Complex numbers support all the regular arithmetic operations. You can figure them out yourself, so long as you remember i^2 = -1. In the complex plane, addition looks like vector addition, and multiplying by an imaginary number is a rotation.

ColinWright 14y ago

>> line that gets mapped to itself > So a trivial example might be a > 360 degree rotation? That's a very trivial example, and therefore good. Less trivial examples are a sheer, an expansion, or a rotation in 3D space. A rotation in 2D space apparently only leaves the origin fixed, and that's where we need complex numbers. To find a fixed line in that case we need to find roots of a quadratic with negative discriminant, hence needing sqrts of negative numbers.