It's been so long since I thought about this, I just need to know if this is correct.(adsbygoogle = window.adsbygoogle || []).push({});

If I have the matrix representation of a linear transformation between vector spaces V and W, and I take the transpose of the matrix, am I in essence constructing the matrix representation of a corresponding transformation from W* to V* (where * denotes dual space)?

And if I take the transpose of a row vector in V, can I think of the resulting column vector as an element of V*?

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

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!

# Vectors, dual vectors

**Physics Forums | Science Articles, Homework Help, Discussion**