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Explain Like I’m Five @lemmy.ml
meowmeowmeow @lemmy.ml

Eilf: Matrix stuff

  1. Determinant of a matrix
  2. Difference between inverse matrix and identity matrix and what are they?
  3. Eigenvalues
  4. Unitary or orthonormal matrix
  5. Diagonal matrix
  6. How to compute matrices?

Thank you in advance for answering anyone of them.

10 comments

  • @meowmeowmeow

    1. A good way to think of matrices is as a kind of function. They take column vectors as "input” by multiplying with them, and the "output" from that product is another vector. The determinant measures how much a matrix stretches the space the input vectors come from. Big determinants stretch spaces way out, small ones shrink them way down, and negative ones reverse them like a mirror.

    • @meowmeowmeow
      2(a). In a lot of mathematical systems, the "identity" is the thing that "does nothing." For example, when adding ordinary numbers the identity is 0 because adding 0 to any number does nothing - the other number stays the same. Similarly, when multiplying the identity is 1 because multiplying 1 with any number also does nothing. The identity matrix plays the same role - if you multiply any (square) matrix with the identity, you'll get back the same matrix you started with.

      • @meowmeowmeow
        2(b). The inverse is related to the identity. It's sort of the "opposite" of a math object (a number, matrix, etc.) but in a specific way. When combining something with its inverse by some operation (like adding or multiplying) the result is the identity. For example: when adding, the inverse of x is -x because x+(-x) = 0. And when multiplying, the inverse of x is 1/x because x1/x = 1. In the same way, when a matrix multiplies with its inverse, the result is the identity matrix.

10 comments