OpenMath Content Dictionary: linalg2col

Canonical URL:
http://www.openmath.org/cd/linalg2col.ocd
CD Base:
http://www.openmath.org/cd
CD File:
linalg2col.ocd
CD as XML Encoded OpenMath:
linalg2col.omcd
Defines:
matrix, matrixcolumn, vector
Date:
2004-11-30
Version:
4 (Revision 1)
Review Date:
2006-11-30
Status:
experimental


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This CD treats matrices and vectors in a column oriented fashion (using matrixcolumns). November 2004: A.M. Cohen edited this CD with the following consequences: -- This CD was formerly named linalg3. The current name linalg2col refers to the resemblance with linalg2. As a consequence all (further) occurrences of linalg3 in this CD have been replaced by linalg2col. -- Two CMPs and two FMPs are added to the symbol vector. Lack of expressive power limits the FMP statements to 3-dimensional arrays.


vector

Role:
application
Description:

This symbol represents an n-ary function used to construct (or describe) vectors. Vectors in this CD are considered to be column vectors, and must therefore be transposed to be considered as row vectors.

Example:
An example of vector using n arguments. The specific vector constructed in this example is transpose of [3,6,9].
vector ( 3 , 6 , 9 )
Commented Mathematical property (CMP):
The transpose of a linalg2col.vector is a linalg2.vector
Formal Mathematical property (FMP):
a , b , c . vector ( a , b , c ) T = ( a , b , c )
Commented Mathematical property (CMP):
The transpose of a linalg2.vector is a linalg2col.vector
Formal Mathematical property (FMP):
a , b , c . ( a , b , c ) T = vector ( a , b , c )
Signatures:
sts


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matrixcolumn

Role:
application
Description:

This symbol is an n-ary constructor used to represent columns of matrices. Its arguments should be members of a ring.

Example:
Representation of a column of a matrix of length two containing the integers [1,0]
matrixcolumn ( 1 , 0 )
Signatures:
sts


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matrix

Role:
application
Description:

This symbol is an n-ary matrix constructor which requires matrixcolumn's as arguments. It is used to represent matrices.

Example:
Representation of a 2x2 identity matrix
matrix ( matrixcolumn ( 1 , 0 ) , matrixcolumn ( 0 , 1 ) )
Signatures:
sts


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