Example: Find the polynomials for u, v, and c, where c is the greatest common divisor of a and b such that:

u( x2 + 1) + v( x – 1) = c

Command:

EGCD(X^2+1,X-1)

 

 

 

 

 

Result:

{2,1,-(X+1)}

 

 

 

 

 

See also:

IEGCD, ABCUV

 

 

 

 

 

EGV

Command

 

 

 

 

 

Type:

 

 

 

 

 

Description:

Eigenvalues and Eigenvectors Command: Computes the eigenvalues and right eigenvectors for a

 

square matrix.

 

 

 

 

 

 

The resulting vector EVal contains the computed eigenvalues. The columns of matrix EVec

 

contain the right eigenvectors corresponding to the elements of vector EVal.

 

The computed results should minimize (within computational precision):

 

 

 

 

A EVec EVec diag( EVal)

 

 

 

 

 

 

 

 

 

 

 

 

 

------------------------------------------------------------------------------

 

 

 

 

 

 

 

n

A

 

 

 

 

 

where diag (EVal) denotes the n × n diagonal matrix containing the eigenvalues EVal.

Access:

!Ø LEIGENVECTOR EGV

 

( Ø is the left-shift of the 5key).

 

MATRIX LEGV

 

( ´is the left-shift of the Pkey).

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

 

 

Level 2/Item 1

Level 1/Item 2

 

 

 

 

 

 

 

 

 

 

 

 

[[matrix ]]A

 

 

[[matrix ]]EVec

[vector ]EVal

See also:

EGVL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EGVL

Command

 

 

 

 

 

Type:

 

 

 

 

 

Description:

Eigenvalues Command: Computes the eigenvalues of a square matrix.

 

 

The resulting vector L contains the computed eigenvalues.

 

Access:

!Ø LEIGENVECTOR EGVL

 

( Ø is the left-shift of the 5key).

 

MATRIX LEGVL

 

( ´is the left-shift of the Pkey).

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

 

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

 

 

[[matrix ]]A

 

 

[vector ]EVal

See also:

EGV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ELSE

Command

 

 

 

 

 

Type:

 

 

 

 

 

Description:

ELSE Command: Starts false clause in conditional or error-trapping structure.

 

See the IF and IFERR keyword entries for more information.

 

Access:

BRANCH IF ELSE

 

( °is the left-shift of the Nkey).

Input/Output:

None

 

 

 

 

 

See also:

IF, CASE, DO, ELSE, IFERR, REPEAT, THEN, UNTIL, WHILE

 

 

 

 

 

 

 

 

 

 

 

END

Command

 

 

 

 

 

Type:

 

 

 

 

 

Description:

END Command: Ends conditional, error-trapping, and indefinite loop structures.

Full Command and Function Reference 3-73