what is a matrix

[reverse]

Hi guys…I’m kind of interested in the concept of the matrix…from the point of view that it’s a good way to represent the real world using numbers.

 

Might be useful for creating an A.I. processing stack or something like that.

Maybe even a matrix of matricis…think really big.

 

So,

 

is a bar graph a matrix?

 

can you have a matrix in more that three dimensions?

 

Like, could you have a matrix that evolves to another over time?

[Dave]

is a bar graph a matrix?

 

No - it's a bar graph It might be possible for a bar chart to be represented as a matrix, although I don't see how that could be useful at all.

 

can you have a matrix in more that three dimensions?

 

Sure:

 

[math]I_4 = \left( \begin{array}{cccc}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & 1 & 0\\

0 & 0 & 0 & 1

\end{array}\right)[/math]

 

Like, could you have a matrix that evolves to another over time?

 

If time was denoted by some variable [math]t[/math], then sure, why not? For instance, the matrix:

 

[math]\left( \begin{array}{cc}

t & 0\\

0 & \sin(t)

\end{array}\right)[/math]

 

is dependent upon time. Matrices are in fact quite important/have a role in solutions of systems of ordinary differential equations - a lot of these are certainly dependent upon time.

 

The major role of matrices that springs to mind for me has to be something like digital signal processing. Although I'm not technically proficient to tell you how matrices play a part in this, I do know that they're very important.

[reverse]

so say you got abstract.

 

get a 10 story building with 10 offices each with a phone.

 

give each person in that office tower an equation to do.

 

and then to ring the answer to another specified office.

 

 

would you consider that a three dimensional matrix?

 

what if they were just gears instead of people?

 

what if they were cleverly organized Microsoft XL spreadsheets..

 

what if they were crystal stacks being interlaced with lasers and the nodes calculated with phototransistors.

 

all matricis??