HP 48gII - Manual (Page 375)

Page 11-49
Function contained in this menu are: LQ, LU, QR,SCHUR, SVD, SVL.
Function LU
Function LU takes as input a square matrix A, and returns a lower-triangular
matrix L, an upper triangular matrix U, and a permutation matrix P, in stack
levels 3, 2, and 1, respectively. The results L, U, and P, satisfy the equation
P⋅A = L⋅U. When you call the LU function, the calculator performs a Crout
LU decomposition of
A using partial pivoting.
For example, in RPN mode: [[-1,2,5][3,1,-2][7,6,5]] LU
produces:
3:[[7 0 0][-1 2.86 0][3 –1.57 –1]
2: [[1 0.86 0.71][0 1 2][0 0 1]]
1: [[0 0 1][1 0 0][0 1 0]]
In ALG mode, the same exercise will be shown as follows:
Orthogonal matrices and singular value decomposition
A square matrix is said to be orthogonal if its columns represent unit vectors
that are mutually orthogonal. Thus, if we let matrix
U = [v
1
v
2
… v
n
] where
the v
i
, i = 1, 2, …, n, are column vectors, and if v
i
• v
j
= δ
ij
, where δ
ij
is the
Kronecker’s delta function, then U will be an orthogonal matrix. This
conditions also imply that U⋅ U T = I.