^{}This may be a silly question, but if I have an 8x3 matrix(adsbygoogle = window.adsbygoogle || []).push({}); X, for example, then the rows of this matrix will span R3 (and will be linearly dependent). When we find the solution to:

Xw=t

wheretis an 8x1 matrix of t's. Then each row can be represented as

[itex]w_{1}[/itex][itex]x_{i1}[/itex]+[itex]w_{2}[/itex][itex]x_{i2}[/itex]+[itex]w_{3}[/itex][itex]x_{i3}[/itex] = [itex]t[/itex].

Each row then forms a unique plane in R3, correct? Does the matrixXwform a plane? I'm learning about Perceptrons, a form of Artificial Neural Network, in which each row of data is classified as either

[itex]y^{'}[/itex] = +1 or -1 depending on if [itex]w_{1}[/itex][itex]x_{i1}[/itex]+[itex]w_{2}[/itex][itex]x_{i2}[/itex]+[itex]w_{3}[/itex][itex]x_{i3}[/itex] > [itex]t[/itex] or [itex]w_{1}[/itex][itex]x_{i1}[/itex]+[itex]w_{2}[/itex][itex]x_{i2}[/itex]+[itex]w_{3}[/itex][itex]x_{i3}[/itex] < [itex]t[/itex].

The book states that in the above situation, "The perceptron model [in the example above] is linear in its parameterswandx. Because of this, the decision boundary of a perceptron, which is obtained by setting [itex]y^{'}[/itex]=0, is a linear hyperplane that separates the data into two classes, -1 and +1."

I'm having a really hard time understanding what this quote is trying to say, because I don't see howXw=0"forms a hyperplane" in x-space.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Understanding Ax=b

Loading...

Similar Threads - Understanding Ax=b | Date |
---|---|

I Understanding Hilbert Vector Spaces | Mar 2, 2018 |

B Help understanding a proof | Jun 8, 2017 |

I Problem understanding the SPAN | May 1, 2017 |

I Trying to understand least squares estimates | Feb 25, 2017 |

Having difficulty with an Ax=b problem and understanding it | Jul 7, 2008 |

**Physics Forums - The Fusion of Science and Community**