Owner's Manual

812 Appendix A: Functions and Instructions
e ^( squareMatrix1 ) ⇒
⇒⇒
⇒ squareMatrix
Returns the matrix exponential of squareMatrix1 .
This is
not the same as calculating e raised to the
power of each element. For information about the
calculation method, refer to
cos().
squareMatrix1 must be diagonalizable. The result
always contains floating-point numbers.
e ^([1,5,3;4,2,1;6,ë 2,1]) ¸
⎣
⎣⎣
⎣
⎢
⎢⎢
⎢
⎡
⎡⎡
⎡
⎦
⎦⎦
⎦
⎥
⎥⎥
⎥
⎤
⎤⎤
⎤
782.209 559.617 456.509
680.546 488.795 396.521
524.929 371.222 307.879
eigVc() MATH/Matrix menu
eigVc( squareMatrix ) ⇒
⇒⇒
⇒ matrix
Returns a matrix containing the eigenvectors for
a real or complex
squareMatrix , where each
column in the result corresponds to an
eigenvalue. Note that an eigenvector is not
unique; it may be scaled by any constant factor.
The eigenvectors are normalized, meaning that if
V = [x
1
, x
2
, … , x
n
], then:
x
1
2
+ x
2
2
+ … + x
n
2
= 1
squareMatrix is first balanced with similarity
transformations until the row and column norms
are as close to the same value as possible. The
squareMatrix is then reduced to upper Hessenberg
form and the eigenvectors are computed via a
Schur factorization.
In Rectangular complex format mode:
[L1,2,5;3,L6,9;2,L5,7]! m1 ¸
⎣
⎣⎣
⎣
⎢
⎢⎢
⎢
⎡
⎡⎡
⎡
⎦
⎦⎦
⎦
⎥
⎥⎥
⎥
⎤
⎤⎤
⎤
ë 1 2 5
3 ë 6 9
2 ë 5 7
eigVc(m1) ¸
⎣
⎣⎣
⎣
⎢
⎢⎢
⎢
⎡
⎡⎡
⎡
⎦
⎦⎦
⎦
⎥
⎥⎥
⎥
⎤
⎤⎤
⎤
ë.800… .767… .767…
.484… .573…+.052…ø
i
ii
i .573…ì.052…ø i
ii
i
.352… .262…+.096…ø i
ii
i .262…ì.096…ø i
ii
i
eigVl() MATH/Matrix menu
eigVl( squareMatrix ) ⇒
⇒⇒
⇒ list
Returns a list of the eigenvalues of a real or
complex
squareMatrix .
squareMatrix is first balanced with similarity
transformations until the row and column norms
are as close to the same value as possible. The
squareMatrix is then reduced to upper Hessenberg
form and the eigenvalues are computed from the
upper Hessenberg matrix.
In Rectangular complex format mode:
[L1,2,5;3,L6,9;2,L5,7]! m1 ¸
⎣
⎣⎣
⎣
⎢
⎢⎢
⎢
⎡
⎡⎡
⎡
⎦
⎦⎦
⎦
⎥
⎥⎥
⎥
⎤
⎤⎤
⎤
ë 1 2 5
3 ë 6 9
2 ë 5 7
eigVl(m1)
¸
{ë4.409… 2.204…+.763…ø i
2.204…ì.763…
ø i }
Else See If, page 826.
ElseIf CATALOG See also If, page 826.
If Boolean expression1 Then
block1
ElseIf
Boolean expression2 Then
block2
©
ElseIf
Boolean expressionN Then
blockN
EndIf
©
ElseIf
can be used as a program instruction for
program branching.
Program segment:
©
:If choice=1 Then
: Goto option1
: ElseIf choice=2 Then
: Goto option2
: ElseIf choice=3 Then
: Goto option3
: ElseIf choice=4 Then
: Disp "Exiting Program"
: Return
:EndIf
©
EndCustm See Custom, page 800.