Re: [math-fun] Heron's formula/Cayley-Menger determinant
Matrix III isn't real. a,b,c are the side _vectors_ as complex numbers. At 11:02 PM 6/29/2012, Pacher Christoph wrote:
Henry Baker wrote:
Matrix III is also a rare example of a _symmetric_ complex matrix that is _not Hermitian_.
Isn't a symmetric matrix A Hermitian iff A is real symmetric ?!
Christoph
On 6/30/12, Henry Baker <hbaker1@pipeline.com> wrote:
Matrix III isn't real. a,b,c are the side _vectors_ as complex numbers.
Fair point --- but in fact, the relevant theorem states that a triangle (simplex) with rational coordinates and edge-lengths which square to integers is embeddable with integer coordinates, so the Heronian label still holds good. WFL
Ooops --- brainstorm. Henry is quite correct --- his triangles are NOT Heronian. Time I had a holiday ... WFL On 6/30/12, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 6/30/12, Henry Baker <hbaker1@pipeline.com> wrote:
Matrix III isn't real. a,b,c are the side _vectors_ as complex numbers.
Fair point --- but in fact, the relevant theorem states that a triangle (simplex) with rational coordinates and edge-lengths which square to integers is embeddable with integer coordinates, so the Heronian label still holds good.
WFL
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Fred lunnon -
Henry Baker