Some time back there was a question about constructing upper triangular matrices. The verbs
below can help. For example,
(1 2 3 4 * id 4) + 8 9 0 0 * (super 4) pr 2
1 0 8 0
0 2 0 9
0 0 3 0
0 0 0 4
NB. Where
id 4
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
super 4
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
pr NB. matrix power
4 : 'x o^:y id # x'"_ 0
(super 4) pr 2
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
o NB. matrix product
+/ .*
(super 4) o super 4
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
id
=...@i.
super
3 : '(2#y) $ 0 , (<: *: y) $ 1 , y#0'
NB. Also
supexp NB. exponential for (number times super n)
3 : '+/(y&pr % !) i.#y'
supexp 0.2 * super 4
1 0.2 0.02 0.00133333
0 1 0.2 0.02
0 0 1 0.2
0 0 0 1
NB. The definition for supexp is a truncated exponential series
NB. which gives the exponential of (number times super n) because
NB. for that matrix the infinite series has zero terms beginning
NB. with the nth. Entries on the kth super diagonal are
NB. (number^k)%!k . supexp is helpful for calculating the
NB. exponential of a general square matrix from its Jordan form.
Kip Murray
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