What real life object, does matrics represent?

[vlad777]

Algebraic vectors (arrays of components) represent geometrical vectors in
Cartesian coordinate system. This I know. And I like how additive sin/cos theorems
make operations with two vectors simple and obvious...
I also know that matrices represent observables in quantum mechanics.
But this is hardly real life object and I also don't understand what observables are.

So what real life object, matrices represent? Please something simple and obvious.

(EDIT: Please someone fix my title : matrics->matrix ; I accidentally pressed enter.)

 

[vlad777]

Also...

If components of a vector are coordinates, what are elements of matrix?

 

[dknguyen]

A matrix is just a way to organize information. The components of a matrix are whatever you are working with. Instead of using multiple equations of ijk vectors, you can just stick them all in a matrix.

So really, the elements in a matrix are terms in an equation.

 

[misterT]

In geometry, you can think of 3x3 matrix as a collection of column vectors. This matrix can then represent a reference coordinate system (coordinate frame).

 

[MrAl]

Algebraic vectors (arrays of components) represent geometrical vectors in
Cartesian coordinate system. This I know. And I like how additive sin/cos theorems
make operations with two vectors simple and obvious...
I also know that matrices represent observables in quantum mechanics.
But this is hardly real life object and I also don't understand what observables are.

So what real life object, matrices represent? Please something simple and obvious.

(EDIT: Please someone fix my title : matrics->matrix ; I accidentally pressed enter.)

Hello,

Matrices are used to represent problems in more than one dimension more compactly than writing everything out. A problem can often be summarized in one dimension but can be expanded to two or more dimensions. As the number of dimensions increases, so do the elements in the matrix increase. For example, a 2x2 matrix might show a problem in 2 dimensions but that same problem in 3 dimensions would require a 3x3 matrix, and in 4 dimensions a 4x4 matrix, etc. We can write the problem out the same thanks to matrices such as the state space equation:
x'=Ax+Bu
where A and B are constant matrices of any dimension 1 or higher
Each row of the matrix represents an equation.

The elements are usually coefficients of variables used in the problem.

 

[squishy36]

One example is that matrices can represent rotations. Look up information on matrix representations of SO(3) for examples.

You'll find that these matrices can be handy for deriving formulas in analytic geometry.

 

[KeepItSimpleStupid]

https://en.wikipedia.org/wiki/Determinant

BTW, those classes were nasty. I used them a lot in solving simultaneous equations while doing electrical circuit analysis. Solving a set of 2 equations and two unknowns by determinants is trivial. Solving 3, 4 and 5 equations with 3, 4 and 5 unknowns is a real pain to do by hand and I had to do that.

 

[squishy36]

Solving a set of 2 equations and two unknowns by determinants is trivial. Solving 3, 4 and 5 equations with 3, 4 and 5 unknowns is a real pain to do by hand and I had to do that.

Well, it was pretty routine if you went to college in the 60's or before (i.e., before calculators and personal computers existed). (Note I'm not being condescending! It's still manual, boring labor.) I'm still a bit taken aback by how calculators have destroyed the arithmetic and elementary plotting abilities of folks of later generations.

Here's an example. My daughter took me to lunch yesterday and wanted to leave a nice tip for the waitress. She intuitively left $5 on a bill that was slightly over $30. She asked me if that was a good tip, then proceeded to use her cell phone to figure out the percentage. Long before she had even typed it in, I told her it was a 16.7% tip. She looked at me amazed and wondered how I did that. 5/30 is 1/6 and I know most of the decimal expansions of fractions from having used them so many times. There was no trick -- just experience.

Another example: another child unit and I were talking and a multiplication like 43*17 came up. I spoke up with the answer, 731, and was looked upon as some savant. How ridiculous! Every child is taught the distributive law, so this is easily rewritten as 43*(10 + 7) = 430 + 301. Even if you can't keep the least significant digits in your head, you can do the major parts and get around 730. When we had to do calculations without calculators, you of course learned these "tricks" or you didn't survive in a technical career.

Another area most kids (and I'm speaking of kids that are, say, under 40 or so) fail in is the ability to generate plots quickly. If there's no computer or plotting calculator around, they're dead in the water. It's a shame they don't learn and practice plotting things by hand. You learn to plot the key points in functions (look for zeros and poles) and, again, approximate the behaviors as necessary. Then sketch the curve; this used to be part of every basic calculus class (do they do this anymore?). Another area is when analyzing a bunch of data from an experiment -- it's pretty easy to grab some graph paper and make a quicky plot. There are all kinds of plots that can be made: a scatter plot, stem and leaf, probability, box and whisker, histogram, etc. While it's nice to use a computer if you can, you shouldn't hesitate to use a hand-plotted graph if no automation is present. Experienced engineers/scientists quickly learn that plotting your data is one of the most important things you can do.

Geez, this turned into a sermon from the old geezer...

 

[KeepItSimpleStupid]

Yep. My favorites are:

You give the cashier $21 for something that costs $11 and she gives you the dollar back because it's too much.

or
A cashier panicing because she typed in the wrong amount and can't make change.

I had a boss who would prime factor license plate numbers while on a trip.

 

[MrAl]

Hi,

You know the more i think about this the more a simple answer comes up.
This question is almost like asking:
"What kind of objects can the universe contain".
Answer:
"Just about anything we know of today".

 

[Jugurtha]

Hello and .. What real life objects, do numbers represent ? None. These are "abstractions".. You go one step above physical and sensory experience to describe them... Can't figure out a maze while you're in.. So you fly above..

"Cold" doesn't physically exist.. But you won't say "This water has less thermic energy than xyz" ..

What does the word "pain" or "pleasure" mean ? What does happiness mean ? These are abstractions to make it EASIER to communicate.. This is the very reason why a word has different meanings when heard by different people.. Each person USES this word as HE PLEASES and NEEDS.

So it's the same thing .. You, Me and an 9 year old boy use same numbers, but to do way different things with them.

I use a matrix with state-space representation, and have used them in differential equations, and so many other things..

They are a TOOL.. To be used as you please or need (both I hope)

 

[misterT]

Hello and .. What real life objects, do numbers represent ? None.

None, and everything. Then again, what can represent a physical object better than the object itself?

 

[Jugurtha]

None, and everything. Then again, what can represent a physical object better than the object itself?

Exactly .. (As an off topic remark, this is why it's not a bright idea to put words on feelings usually.. Words spoil things sometimes)

 

[misterT]

Words spoil things sometimes

Spot on.. just go read this thread: https://www.electro-tech-online.com/threads/ac-flowing-through-a-cap-what-actually-happens.116575/
Warning: Do not reply to that thread, just let it be

 

[MrAl]

Hi again,

Numbers represent objects all the time. We know that the numbers themselves are not the objects themselves, just something to represent them so that we can deal with them more effectively because there are a lot of logical ideas behind numbers. Unless of course the 'information only' theory is correct, in that the objects themselves are actually just groups of information in which case it gets harder to argue that the numbers in theory are not the same as the objects themselves.
For now though i like to stick with numbers simply representing objects, and matrixes are just an extension of numbers as a systematic arrangement of numbers.