Do 3 dimensional matrices exist?

[Rob K]

Hi,

I was just wondering, as I find matrices fascinating, I don't know why, but I was wondering if there was ever a use for 3D ones and if so what would be their application? It just occurred to me as I was reading about holographic hard disc storage.

Curiously

Rob K

 

[micromass]

You should read up on tensors.

 

[Mark44]

A simpler example is a calender, where each page holds the days of a month. The days are arranged in rows of seven days, and each month has four to six rows, not all of which are full.

For example, today's date is Jan. 13, 2012. If we agree that the year is understood to be 2012, we could identify today's date by its position in the week, the week of the month, and the month. So instead of representing it as 1/13, we could represent it as <6, 2, 1>, with 6 being the 6th day of the week, 2 for the 2nd week, and 1 for the first month.

I'm not putting this out there as an improvement on the current scheme for writing dates, but rather as a simple example for motivating three-dimensional matrices.

 

[pwsnafu]

I'm not putting this out there as an improvement on the current scheme for writing dates, but rather as a simple example for motivating three-dimensional matrices.

That motivates 4-D not 3-D. There are only 12 calenders in our system: the calendar that starts on Monday, another that starts with Tuesday, and so on, giving 7. Then double because you need the leap years.

So we have <day of the week, week of the month, month of the year, calendar type>

 

[chiro]

Hey RobK.

Following on what micromass said above, I think you should look at tensor products of matrices. This will help you understand how we create multilinear representations of matrices which allow you to see how we do it for n-dimensions.

 

[dalcde]

You should read up on tensors.

Any recommendations on books for learning tensors?

 

[fedaykin]

Dalcde, I know it's not a book, but this guide helped me out a lot conceptually:

http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

I haven't used tensors very often, so I can't really suggest a book.

 

[dalcde]

Dalcde, I know it's not a book, but this guide helped me out a lot conceptually:

http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

I haven't used tensors very often, so I can't really suggest a book.

Thanks! It looks good.