OpenMath Content Dictionary: linalgspec2

Canonical URL:
http://www.openmath.org/cd/linalgspec2.ocd
CD Base:
http://www.openmath.org/cd
CD File:
linalgspec2.ocd
CD as XML Encoded OpenMath:
linalgspec2.omcd
Defines:
lower_Hessenberg, upper_Hessenberg
Date:
2004-11-30
Version:
3 (Revision 1)
Review Date:
2006-03-30
Status:
experimental


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This CD contains symbols which represent a number of special types of matrix, such as Hessenberg.


upper_Hessenberg

Role:
application
Description:

This symbol represents an upper_Hessenberg matrix, it takes one argument, the argument is a vector of vectors representing the non-zero elements. The first element of the argument specifies the value of the first subdiagonal, the subsequent elements specify the value of the diagonal and subsequent super-diagonals, all other elements are zero.

Example:
A specification of an upper_Hessenberg matrix of dimension 5: [[1 2 3 0 0] [4 5 6 7 0] [0 8 9 10 11] [0 0 12 13 14] [0 0 0 15 16]]
upper_Hessenberg ( ( ( 4 , 8 , 12 , 15 ) , ( 1 , 5 , 9 , 13 , 16 ) , ( 2 , 6 , 10 , 14 ) , ( 3 , 7 , 11 ) ) )
Commented Mathematical property (CMP):
the transpose of an upper_Hessenberg matrix is lower_Hessenberg
Formal Mathematical property (FMP):
upper_Hessenberg ( VV 1 ) T = lower_Hessenberg ( VV 2 )
Signatures:
sts


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lower_Hessenberg

Role:
application
Description:

This symbol represents a lower_Hessenberg matrix, it takes one argument, the argument is a vector of vectors representing the non-zero elements. The first element of the argument specifies the value of the first super-diagonal, the subsequent elements specify the value of the diagonal and subsequent subdiagonals, all other elements are zero.

Example:
A specification of a lower_Hessenberg matrix of dimension 5: [[1 2 0 0 0] [3 4 5 0 0] [6 7 8 9 0] [0 10 11 12 13] [0 0 14 15 16]]
lower_Hessenberg ( ( ( 2 , 5 , 9 , 13 ) , ( 1 , 4 , 8 , 12 , 16 ) , ( 3 , 7 , 11 , 15 ) , ( 6 , 10 , 14 ) ) )
Commented Mathematical property (CMP):
the transpose of a lower_Hessenberg matrix is upper_Hessenberg
Formal Mathematical property (FMP):
lower_Hessenberg ( VV 1 ) T = upper_Hessenberg ( VV 2 )
Signatures:
sts


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