HP Prime Graphing Calculator - Manual (Page 487)

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
1 2 3
4 5 6
7 8 9








3 – 1 0
4 1 – 0
1 – 2 1 –
1 1 – 3 –
0 3 6
0 0 0
,
1 2 3
4 5 6
7 8 9










1 0 0 0 4
7
- 1 0 1 0
1 29
7
--- 2 7 39
7
--- 8 0 278
49
----- 3
7
-
1 2 3
4 5 6
7 8 9










1 0 0
4
1 – 0
1 – 2 1 –
1 0 0
0 3 0
0 0 0 1 2 – 1
0 1 2 –
0 0 1