Function Schur - HP 50g User Manual

Graphing calculator.

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
as a
n m
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
T
that A = Q T Q
, 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
returning a
n m
lower L
trapezoidal matrix, a Q
orthogonal matrix, and a P
n m
m m
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]]
[[-0.91 0.37 -0.18] [-0.36 -0.50 0.79] [-0.20 -0.78 -0.59]]
2:
1: [[0 0 1][0 1 0][1 0 0]]
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