Chaper 1
{
  sentences to get back to:
  	_PAGE_24_
  	When matrices are used to transform from one coordinate system to another in
	Chapter 2, treating the columns of a matrix as a set of vectors will become partic-
	ularly meaningful

  antisymmmetric _ skew symmmetric matrix:
  {
    when transposing signs accross diagonal get flipped on every entry
    diag is always 0
    
  }

  matrix property:
  {
    transp(AB) = transp(B)*transp(A)
    explaining in my own words

    if (A*B)[i][j] =
      p is col count of A == row count of B
      result = 0;
      for k = 0; k < p; ++k)
      {
          result += A[i][k]*B[k][j]
      }

    then if transp(A*B)[i][j] == (A*B)[j][i]
    then (A*B)[j][i] =
      p is col count of A == row count of B
      result = 0;
      for k = 0; k < p; ++k)
      {
          result += A[j][k]*B[k][i] <-

          this can also be written as (B[k][i] *  A[j][k]) because it's just a product
                                        |
                                        |
                                        |
                                        v
                                        transp(B)[i][k] *  transpA[k][j]
                                        so then transp(B) * transp(A)
      }
  }

  law of cosines proof via intersecting chords theorem:
  {
    
    law of cosines proof via dot product
  }

}