HP Prime Graphing NW280AAABA QRmatrix A,var1,var2, SCHURmatrix, Example Schur ⎛⎜ 1 2 ⎞⎟ returns

QR QR Factorization. Factorizes an m×n matrix A numerically as Q*R, where Q is an orthogonal matrix and R is an upper triangular matrix, and returns R. R is stored in var2 and Q=A*inv(R) is stored in var1.

QR(matrix A,var1,var2)

Example:

QR ⎛⎜ 1 2 ⎞⎟ returns ⎝ 3 4 ⎠

⎧

⎨0.3612… 0.9486… ⎩ 0.9486… –0.3162…

,	3.1622… 4.4271		…	,	1 0	⎫
						⎬
	0	0.6324	…		0 1	⎭

SCHUR Schur Decomposition. Factorizes a square matrix into two matrices. If matrix is real, then the result is {[[orthogonal]],[[upper-quasi triangular]]}.

If matrix is complex, then the result is {[[unitary]],[[upper-triangular]]}.

SCHUR(matrix)

Example:

SCHUR ⎛⎜ 1 2 ⎞⎟ returns

⎝ 3 4 ⎠

⎧	0.4159	… 0.9093	…	,
⎨
⎩	0.9093	… 0.4159	…

5.3722…	1	⎫
		⎬
5.55×10–17–0.3722		⎭

SVD Singular Value Decomposition. Factorizes an m × n matrix into two matrices and a vector:

{[[m × m square orthogonal]],[[n × n square orthogonal]], [real]}.

	SVD(matrix)
Example:
	⎛		⎞
		1 2		returns
	⎜		⎟
	SVD ⎝	3 4	⎠
⎧									⎫
	0.4045…	–0.9145…						0.5760… 0.8174…
⎨					,	5.4649… 0.3659…	,		⎬
⎩	0.9145… 0.4045…							0.8174… –0.5760	⎭
484								Matrices