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# Column Vectors

MichaelBartmess.Column Vectors

Datatype | Required | |
---|---|---|

Column Vector A | Real | Yes |

Column Vector B | Real | No |

Column Vector C | Real | No |

Column Vector D | Real | No |

Column Vector E | Real | No |

Column Vector F | Real | No |

Column Vector G | Real | No |

Column Vector H | Real | No |

Column Vector I | Real | No |

Column Vector J | Real | No |

Sum | Avg | Min | Max | |
---|---|---|---|---|

Column Vector A | 44.9 | 8.98 | 1.9 | 12.5 |

Column Vector B | 62.356 | 12.4712 | 1.756 | 22.0 |

Column Vector C | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector D | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector E | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector F | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector G | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector H | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector I | 0.0 | 0.0 | 0.0 | 0.0 |

Column Vector J | 0.0 | 0.0 | 0.0 | 0.0 |

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 Space^{1}

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.