**Last modified:***Wednesday, 21 September 1994***Source code: tensor-quantities.lisp****List of other known theories**

This theory is used to represent vectors of n spatial dimensions which are physical quantities with physical dimensions, such as 'the velocity of particle p'. The theory supports arbitrary numbers of basis vector sets and hence vectors are not isomorphic to n-tuples as is the case in some textbook representations of vectors (Note: Multi-basis vector spaces are essential to many theories such as kinematics). Standard vector operations such as vector addition, scalar multiplication, and scalar or dot product are supported. Operators on vector-quantities must take into account the associated units and dimensions.The theory now also include higher-order tensors.

- (c) 1993, 1994 Gregory R. Olsen and Thomas R. Gruber

**See-Also:**The EngMath paper on line

Basic-Matrix-AlgebraScalar-Quantities

3d-Tensor-Quantities

Matrix-Quantity Numeric-Matrix Orthonormal-Basis Tensor-Quantity Vector-Quantity Unit-Vec Dyad Numeric-Tensor

*+-Basis.DimensionBasis.VecDotDyad-ComponentDyad-Of-DimensionsSpatial.DimensionTensor-OrderTensor-To-MatrixThe-DyadThe-Vector-QuantityThe-Zero-Dyad-Of-TypeThe-Zero-Vector-Of-TypeVector-ComponentVector-Quantities-Of-Dimensions

**The following constants were used from included theories:**

**=<***defined as a***relation***in theory***Kif-Numbers****Abelian-Group***defined as a***relation***in theory***Abstract-Algebra****Arity***defined as a***function***in theory***Frame-Ontology****Class***defined as a***class***in theory***Frame-Ontology****Column-Dimension***defined as a***function***in theory***Basic-Matrix-Algebra****Constant-Quantity***defined as a***class***in theory***Physical-Quantities****Defined***defined as a***class***in theory***Kif-Extensions****Dimensionless-Quantity***defined as a***class***in theory***Physical-Quantities****Distributes***defined as a***relation***in theory***Abstract-Algebra****Documentation***defined as a***relation***in theory***Frame-Ontology****Domain***defined as a***relation***in theory***Frame-Ontology****Function***defined as a***class***in theory***Kif-Relations****Identity-Dimension***defined as a***object***in theory***Physical-Quantities****Identity-Matrix***defined as a***class***in theory***Basic-Matrix-Algebra****Magnitude***defined as a***function***in theory***Physical-Quantities****Matrix***defined as a***class***in theory***Basic-Matrix-Algebra****Member***defined as a***relation***in theory***Kif-Sets****Non-Negative-Integer***defined as a***class***in theory***Kif-Extensions****Nth-Domain***defined as a***relation***in theory***Frame-Ontology****Physical-Dimension***defined as a***class***in theory***Physical-Quantities****Physical-Quantity***defined as a***class***in theory***Physical-Quantities****Positive-Integer***defined as a***class***in theory***Kif-Extensions****Quantity.Dimension***defined as a***function***in theory***Physical-Quantities****Range***defined as a***relation***in theory***Frame-Ontology****Row-Dimension***defined as a***function***in theory***Basic-Matrix-Algebra****Row-Matrix***defined as a***class***in theory***Basic-Matrix-Algebra****Scalar-Quantity***defined as a***class***in theory***Scalar-Quantities****Size***defined as a***function***in theory***Basic-Matrix-Algebra****Square-Matrix***defined as a***class***in theory***Basic-Matrix-Algebra****Subclass-Of***defined as a***relation***in theory***Frame-Ontology****Summation***defined as a***function***in theory***Physical-Quantities****Superclass-Of***defined as a***relation***in theory***Frame-Ontology****The-Zero-Scalar-For-Dimension***defined as a***function***in theory***Scalar-Quantities****Transpose***defined as a***function***in theory***Basic-Matrix-Algebra****Unit-Of-Measure***defined as a***class***in theory***Physical-Quantities****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**

**All constants that were mentioned were defined.**

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