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Appendix A: Functions and Instructions 815
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
.573…ì.052…ø
i
.352… .262…+.096…ø
i
.262…ì.096…ø
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 830.
ElseIf CATALOG See also If, page 830.
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 802.
EndDlog See Dialog, page 810.
EndFor See For, page 822.
EndFunc See Func, page 823.
EndIf See If, page 830.