HP Prime Graphing NW280AAABA manual HessenbergMtrxA, 278, IsmithMtrxA, Ismith ⎜

Hessenberg Matrix reduction to Hessenberg form. Returns [P,B] such that B=inv(P)*A*P.

hessenberg(Mtrx(A))

Example:	⎛		⎞
		1 2 3
	⎜		⎟
In CAS view, hessenberg ⎜		4 5 6	⎟
	⎜		⎟
	⎝	7 8 9	⎠

returns

		4
	0
1 0 0
		- 1
		7

2939

1--- 2 7 --- 8

7 7

0 1 0

	278	3
0 -----		-
	49	7

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:
			⎛			⎞
				1 2 3
			⎜			⎟
ismith ⎜				4 5 6		⎟ returns
			⎜			⎟
			⎝	7 8 9		⎠
		0	0
	1				1 0 0		1 –2 1
	4	–1 0			0 3 0		0 1 –2
	–1 2		–1		0 0 0		0 0 1

482 Matrices