Hey guys, I'm studying these concepts in linear algebra right now and I was wanting to confirm that my interpretation of it was correct.(adsbygoogle = window.adsbygoogle || []).push({});

One to one in algebra means that for every y value, there is only 1 x value for that y value- as in- a function must pass the horizontal line test (Even functions, trig functions would fail (not 1-1), for example, but odd functions would pass (1-1))

Onto means that in a function, every single y value is used, so again, trig and event functions would fail, but odd functions would pass- Any kind of function with a vertical asymptote would pass

So i tried to put these concepts in the context of linear functions and this is what I'm thinking-

Since transformations are represented by matrices,

Linearly independent transformation matrices would be considered one to one- because they have a unique solution. Linearly dependent transformations would not be one-to-one because they have multiple solutions to each y(=b) value, so you could have multiple x values for b

Now for onto, I feel like if a linear transformation spans the codomain it's in, then that means that all b values are used, so it is onto.

Examples:

1-1 but not onto

A linearly independent transformation from R3->R4 that ends up spanning only a plane in R4

Onto but not 1-1

A linearly dependent transformation from R3->R2 thats spans R2

1-1 AND onto

A linearly independent transformation from R3->R3 that spans R3

Neither 1-1 nor onto

A linearly dependent transformation from R2->R2 that spans a line

Is this interpretation correct?

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

Join Physics Forums Today!

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

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

# Linear Algebra- Onto and One to One Linear Transformations

Loading...

Similar Threads - Linear Algebra Onto | Date |
---|---|

I Geometric intuition of a rank formula | Feb 8, 2018 |

I Tensors vs linear algebra | Jan 28, 2018 |

I Is there a geometric interpretation of orthogonal functions? | Jan 25, 2018 |

I Diagonalization and change of basis | Jan 16, 2018 |

I A different way to express the span | Nov 26, 2017 |

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