HP 50g Graphing Calculator - Manual (Page 378)

Page 11-51
decomposition, while the vector s represents the main diagonal of the matrix S
used earlier.
For example, in RPN mode: [[5,4,-1],[2,-3,5],[7,2,8]] SVD
3: [[-0.27 0.81 –0.53][-0.37 –0.59 –0.72][-0.89 3.09E-3 0.46]]
2: [[ -0.68 –0.14 –0.72][ 0.42 0.73 –0.54][-0.60 0.67 0.44]]
1: [ 12.15 6.88 1.42]
Function SVL
Function SVL (Singular VaLues) returns the singular values of a matrix A
n ×m
as a
vector s whose dimension is equal to the minimum of the values n and m. For
example, in RPN mode,
[[5,4,-1],[2,-3,5],[7,2,8]] SVL
produces [ 12.15 6.88 1.42].
Function SCHUR
In RPN mode, function SCHUR produces the Schur decomposition of a square
matrix A returning matrices Q and T, in stack levels 2 and 1, respectively, such
that A = Q
⋅T⋅Q T
, where Q is an orthogonal matrix, and T is a triangular
matrix. For example, in RPN mode,
[[2,3,-1][5,4,-2][7,5,4]] SCHUR
results in:
2: [[0.66 –0.29 –0.70][-0.73 –0.01 –0.68][ -0.19 –0.96 0.21]]
1: [[-1.03 1.02 3.86 ][ 0 5.52 8.23 ][ 0 –1.82 5.52]]
Function LQ
The LQ function produces the LQ factorization of a matrix A
n ×m
returning a
lower L
n ×m
trapezoidal matrix, a Q
m ×m
orthogonal matrix, and a P
n ×n
permutation matrix, in stack levels 3, 2, and 1. The matrices A, L, Q and P
are related by P
⋅A = L⋅Q. (A trapezoidal matrix out of an n×m matrix is the
equivalent of a triangular matrix out of an n ×n matrix). For example,
[[ 1, -2, 1][ 2, 1, -2][ 5, -2, 1]] LQ
produces
3: [[-5.48 0 0][-1.10 –2.79 0][-1.83 1.43 0.78]]
2: [[-0.91 0.37 -0.18] [-0.36 -0.50 0.79] [-0.20 -0.78 -0.59]]
1: [[0 0 1][0 1 0][1 0 0]]