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Matrices 483
Hermite Hermite normal form of a matrix with coefficients in Z:
returns U,B such that U is invertible in Z, B is upper
triangular and B=U*A.
ihermite(Mtrx(A))
Example:
ihermite returns
Hessenberg Matrix reduction to Hessenberg form. Returns [P,B] such
that B=inv(P)*A*P.
hessenberg(Mtrx(A))
Example:
In CAS view, hessenberg
returns
Smith Smith normal form of a matrix with coefficients in Z:
returns U,B,V such that U and V invertible in Z, B is
diagonal, B[i,i] divides B[i+1,i+1], and B=U*A*V.
ismith(Mtrx(A))
Example:
ismith returns
123
456
789
3– 10
41– 0
1– 21–
11– 3–
03 6
00 0
,
123
456
789
100
0
4
7
-1
010
1
29
7
---2 7
39
7
---8 0
278
49
-----
3
7
-
123
456
789
100
41– 0
1– 21–
100
030
000
12– 1
01 2–
00 1