41CL Quiz: Determinant of 30x30 anti-Identity matrix

[Valentin Albillo]

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Self-quote to add numerical examples to what I said in my previous post:

(05-19-2018 04:50 AM)Valentin Albillo Wrote:  For the "anti-identity" matrices, the first that gives a non-integer determinant is the 5x5 case (12-digit HP-71B/Math ROM, 15-digit internally.)

Anti-identity:

>MAT DISP A;

      0 1 1 1 1
      1 0 1 1 1
      1 1 0 1 1
      1 1 1 0 1
      1 1 1 1 0

>DET(A)

      3.99999999999

Up to 30x30, the maximum error is found for the 10x10 case:

      Det = -9.00000000003

Quote:I've readily found 5x5 and 4x4 cases with non-integer determinants, some of them quite peculiar.

5x5 case:

>MAT DISP A;

      1 0 1 1 1
      1 1 0 1 0
      0 1 0 1 1
      1 1 1 0 1
      0 1 1 1 0

>DET(A)

      5.00000000001

4x4 case:

This one is most peculiar:

>MAT DISP A;

      0 0 0 1
      0 0 1 0
      1 1 1 1
      1 1 1 0

>DET(A)

      1.E-24 (!!)

3x3 case:

>MAT DISP A;

      1 1 1
      0 0 1
      1 1 0

>DET(A)

      -.000000000001

2x2 case: (1-3 elements)

>MAT DISP A;

      1 2
      3 1

>DET(A)

      -5.00000000001

And this deserves a full facepalm or two:

>MAT DISP A;

      3 1
      3 1

>DET(A)

      .000000000003

Of course the exact determinant is 0 because both rows are identical. The fact that it does not detect it but instead goes on a spree using a full-drawn algorithm with pivot(s) and such for so ultra-simple a case it truly astounding.

Best regards and have a nice weekend.
V.
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