Theory BASIC-MATRIX-ALGEBRA

• Last modified: Tuesday, 5 July 1994
• Source code: basic-matrix.lisp
• List of other known theories

Theory documentation:

This theory attempts to capture basic concepts in linear algebra, with emphasis on matrix operations. Definitions are derived from, Strang, G., Linear Algebra and its Applications, 3rd Edition, Harcourt Brace Jovanovich, 1988.

Notes:

• (c) 1993, 1994 Gregory R. Olsen, Yves Peligry, and Thomas R. Gruber
  
• See-Also: The EngMath paper on line
  

Cross Reference Report:

Theories included by Basic-Matrix-Algebra:

  Frame-Ontology

Theories that include Basic-Matrix-Algebra:

  Tensor-Quantities

9 classes defined:

    Matrix
       Row-Matrix
       Column-Matrix
       Square-Matrix
          Identity-Matrix
          Diagonal-Matrix
          Invertible-Matrix
          Orthogonal-Matrix
       Diagonal-Matrix
    Zero-Element

No relations defined.

17 functions defined:

  *
  +
  -
  Cofactor
  Column
  Column-Dimension
  Determinant
  Matrix-Inverse
  Matrix-Less-Column
  Matrix-Less-Row
  Matrix-Less-Row-And-Column
  Matrix-Of-Columns
  Matrix-Of-Rows
  Row
  Row-Dimension
  Size
  Transpose

No instances defined.

The following constants were used from included theories:

• < defined as a relation in theory Kif-Numbers
• =< defined as a relation in theory Kif-Numbers
• >= defined as a relation in theory Kif-Numbers
• Arity defined as a function in theory Frame-Ontology
• Class defined as a class in theory Frame-Ontology
• Defined defined as a class in theory Kif-Extensions
• Documentation defined as a relation in theory Frame-Ontology
• Domain defined as a relation in theory Frame-Ontology
• Expt defined as a function in theory Kif-Numbers
• Function defined as a class in theory Kif-Relations
• Item defined as a relation in theory Kif-Lists
• Length defined as a function in theory Kif-Lists
• Nth defined as a function in theory Kif-Lists
• Nth-Domain defined as a relation in theory Frame-Ontology
• Positive-Integer defined as a class in theory Kif-Extensions
• Range defined as a relation in theory Frame-Ontology
• Same-Values defined as a relation in theory Frame-Ontology
• Subclass-Of defined as a relation in theory Frame-Ontology
• Undefined defined as a class in theory Kif-Extensions
• Value defined as a function in theory Kif-Relations
• Value-Cardinality defined as a function in theory Frame-Ontology
• Value-Type defined as a relation in theory Frame-Ontology

The following constants were used from theories not included:

• Summation defined as a function in theory Physical-Quantities

All constants that were mentioned were defined.