Need good reference on multilinear algebra

I'd like to find a decent text on multilinear algebra in its full
generality - e.g. involving tensors. One that gives some sort of
insight into how multilinear algebra ties into exterior algebra would
be nice.

For instance, I'm trying to figure out what the relationship between
multivectors and tensors are - is it that multivectors are tensors
that satisfy certain properties? Is it that multivectors are
equivalence classes of tensors? A reference to address these sorts of
questions, which have come up a lot for various music-related reasons
over the past few months, would be nice.

If anyone knows of one I'd much appreciate it!

Thanks
-Mike

Hi Mike,
maybe J.Lawson's course syllabus about differential geometry could be what you are looking for:
https://www.math.lsu.edu/~lawson/
See chapter 9:
https://www.math.lsu.edu/~lawson/Chapter9.pdf
Bye,
Claudi

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'd like to find a decent text on multilinear algebra in its full
> generality - e.g. involving tensors. One that gives some sort of
> insight into how multilinear algebra ties into exterior algebra would
> be nice.
>
> For instance, I'm trying to figure out what the relationship between
> multivectors and tensors are - is it that multivectors are tensors
> that satisfy certain properties? Is it that multivectors are
> equivalence classes of tensors? A reference to address these sorts of
> questions, which have come up a lot for various music-related reasons
> over the past few months, would be nice.
>
> If anyone knows of one I'd much appreciate it!
>
> Thanks
> -Mike
>

Hi Mike,

I found this online book:

Linear Algebra via Exterior Products: book web site

https://sites.google.com/site/winitzki/linalg

In chapter 1 he introduces tensor products and in chapter2
the exterior product is defined as a special case of tensor products.
Hope this helps.

Denis

PS: I'm the denix13 silently idling on IRC: I am just an amateur
of musical mathematics and I prefer to remain silent for now as I
have a lot to learn. Thank you and keep up the good work!

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'd like to find a decent text on multilinear algebra in its full
> generality - e.g. involving tensors. One that gives some sort of
> insight into how multilinear algebra ties into exterior algebra would
> be nice.
>
> For instance, I'm trying to figure out what the relationship between
> multivectors and tensors are - is it that multivectors are tensors
> that satisfy certain properties? Is it that multivectors are
> equivalence classes of tensors? A reference to address these sorts of
> questions, which have come up a lot for various music-related reasons
> over the past few months, would be nice.
>
> If anyone knows of one I'd much appreciate it!
>
> Thanks
> -Mike
>

--- In tuning-math@yahoogroups.com, "Denix" <denix13@...> wrote:
>
>
>
>
> Hi Mike,
>
> I found this online book:
>
> Linear Algebra via Exterior Products: book web site
>
> https://sites.google.com/site/winitzki/linalg

I put that in the "files" section on this group a while back, in the "books" directory.

*Mike:*
*Here is one on line on tensors if it may help. He also has one on
electrodynamics and relativity if interested.*
*http://samizdat.mines.edu/tensors/ShR6b.pdf*
*ƒg
*
On Thu, May 10, 2012 at 3:42 PM, Mike Battaglia <battaglia01@gmail.com>wrote:

> **
>
>
> I'd like to find a decent text on multilinear algebra in its full
> generality - e.g. involving tensors. One that gives some sort of
> insight into how multilinear algebra ties into exterior algebra would
> be nice.
>
> For instance, I'm trying to figure out what the relationship between
> multivectors and tensors are - is it that multivectors are tensors
> that satisfy certain properties? Is it that multivectors are
> equivalence classes of tensors? A reference to address these sorts of
> questions, which have come up a lot for various music-related reasons
> over the past few months, would be nice.
>
> If anyone knows of one I'd much appreciate it!
>
> Thanks
> -Mike
>
>

Hi - just realized I never wrote a proper thanks for all these
references so - thanks! I'll be slowly working my way through them.

-Mike

On Fri, May 11, 2012 at 1:46 PM, Freeman Gilmore
<freeman.gilmore@gmail.com> wrote:
>
> Mike:
> Here is one on line on tensors if it may help.   He also has one on electrodynamics and relativity if interested.
> http://samizdat.mines.edu/tensors/ShR6b.pdf
> ƒg