# Column Vectors

Not Reviewed
Type
Dataset
Category
vCommons
Contents
10 columns
Tags:
Rating
ID
MichaelBartmess.Column Vectors
UUID
4f979586-98cc-11e4-a9fb-bc764e2038f2
Columns
DatatypeRequired
Column Vector ARealYes
Column Vector BRealNo
Column Vector CRealNo
Column Vector DRealNo
Column Vector ERealNo
Column Vector FRealNo
Column Vector GRealNo
Column Vector HRealNo
Column Vector IRealNo
Column Vector JRealNo
Current statistics
SumAvgMinMax
Column Vector A44.98.981.912.5
Column Vector B62.35612.47121.75622.0
Column Vector C0.00.00.00.0
Column Vector D0.00.00.00.0
Column Vector E0.00.00.00.0
Column Vector F0.00.00.00.0
Column Vector G0.00.00.00.0
Column Vector H0.00.00.00.0
Column Vector I0.00.00.00.0
Column Vector J0.00.00.00.0

This data set contains one to ten column vectors where each column vector can be defined with an arbitrary length.  These column vectors are intended to be used in vector operations that are found within vCalc's Mathematics/Vectors folder.

In most cases vector operations require that any set of column vectors used in a vector operation be of the same dimension; i.e, have the same number of elements.

Note that you can create new vector sets by simply duplicating this data set and using the new data set's UUID as a reference in an equation.

# An Element of a Vector Space1

A vector space is a mathematical structure formed by a collection of elements called vectors. Vectors may be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.

# Euclidean Vectors

An example of a vector space is that of Euclidean vectors.  Euclidean vectors may be used to represent physical quantities such as forces.  Any two Euclidean vectors of the same type of component elements, such as two force vectors, can be added to yield a third, and the multiplication of a force vector by a real multiplier (scalar) is another force vector. In a more geometric sense, vectors representing displacements  in three-dimensional space also form vector spaces.