I have no clue what a matrix is, or what its function is. About the only thing I know, or think I know, is that it is used by some engineers. Please explain in layman’s terms if you have something to share.
It depends.
If you are talking about math, it is a (possibly multidimensional) array of numbers. They can do lots of things like be used to solve systems of linear equations, represent spatial transformations, etc. Search for “linear algebra” and “matrix” and you’ll find a lot.
Or, if you’re a middle manager, then matrix is your oh so special word for a table.
You use them to solve a whole bunch of linear equations in multiple variables at the same time.
Now, yeah, you might say, “Why would I want to do that?”
It’s how you do a CAT scan, that’s why. A CAT scan involves a whole bunch of x-ray slices that give linear data.
(To be really simplistic: suppose that your torso is an oval, and that your spine is toward one side. When you take an x-ray slice from the front, you see something like this: …XXXX… where the X is bone and the … is flesh. But when you take an x-ray slice from one side, you see something like …XXXX… – i.e., the bone is off center.)
Take a whole bunch of these samples from a whole bunch of angles, then use matrix algebra to solve all the equations, and you get a real picture.
Real, practical, productive use for modern arithmetic! Fun, huh?
Trinopus
In simple terms, a matrix is a table of numbers:
0 1 2 4
8 16 32 64
In this case, the matrix is a two-dimensional table with four columns and two rows. Matrices by definition are rectangular, in that every row has the same number of elements as every other row and likewise for the columns.
Matrix algrebra is a defined set of rules that govern matrix manipulation. Generally, matrices can be added, subtracted, multiplied, divided, and so on, just like regular numbers. There are some operations that don’t have equivalent operations in normal algebra, such as cross product (which is a multiplication by rows and columns rather than by individual elements).
Matrices are used in many applications. A computer display is essentially a matrix of pixels; putting graphics on the screen often consists of a set of matrix operations to transform some 3D world scene into two dimensions. Many imaging applications, including Trinopus’ CAT scan, use matrices to represent their data and the operations done on that data. Matrices can be used for solving systems of multiple equations. I’m sure other people will be along to suggest further applications for matrices.
If you want to learn matrix algebra I’d suggest a textbook from an introductory college course. Or search the web for introductionary material. Was there something specific you were wondering, or some particular application?
Learning the other answer to “What is the Matrix?”, of course, requires a fair bit more commitment on your part.
Psst, should we tell him about tensors?
A matrix is a way of organizing information about something. Usually a matrix is used when a just a single number cannot represent something. (BTW a single number is also a matrix of dimension 1x1).
Let me give you an example:
Lets consider the dimensions of your apartment. If you want to just tell someone the total area of your apartment you can say - hey the total area is 2000 sq.ft. or something. Thats a 1x1 matrix, but as you see that does’nt contain much information.
Now, lets say you want to give the dimension of each room in the house too (assume all rooms are rectangular), so you may form a matrix (I donno how to write a matrix here - DOES LATEX CODE WORK HERE ?) but basically you can have say 6 rows of data - row1 can be bedroom1, row two bedroom 2, row 3 can be living room, … etc. and column 1 can be length and column2 can be breath.
Sorry, could’nt come up with a better description. But matrices are used everywhere in math. Vectors are also matrices essentially. So Newton’s laws are vector (matrice) equations.
To be more precise, a matrix always have two dimensions. Vectors have one, and tensors have three. Scalars are dimensionless quantities.
To be more precise yet, a matrix always has 2 dimensions, but either or both can have unit length (thus, 1 is a 1x1 matrix). One uses it, ultimately, for a variety of purposes, most of which center around systems of equations. If, for example, you have a system of linear equations, you can represent it conveniently with matrices, which means you can solve it conveniently using matrix algebra.
Vectors can be represented by matrices with one dimension being of unit size (i.e. [1,2,3]). Tensors can have any number of indices one wants, however; a vector is a rank one tensor, a scalar is rank zero tensor, and neither is a matrix per se, since tensors have defined transformation properties which matrices need not have (matrices, in the final analysis, being merely a way of organizing numbers which needn’t have any relation to each other).
To be even more precise, vectors are tensors too.
moejack, you want to know anything about Keanu Reeves?
Matices can be use to describe a circuit. It is easier (ep for a computer) to figure out the resistance between two nodes with a matrix than with series/parallell/delta/wye calculations.
Brian
I am used as a moderator for the General Questions forum. Hope this helps.
Aren’t operations done on matrices of binary digits (ones and zeros) how normal, everyday calculators… uh… calculate?
Here is what I have obtained from all of your posts:
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Matrices are fun, convenient ways of solving a system of linear equations, among other things.
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You all think it is funny to talk about Vectors, and Tensors to attempt to confuse me and make me feel like more of an idiot than I already do.
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Dr.Matrix has quite a quick wit. Hmmmm.
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I should avoid matrices for the rest of my life.
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Keanu Reaves, despite having some knowledge of “The Matrix” is still one of the worst actors to have appeared on screen.
For a newbie, I think moejuck is very quickly getting the hang of this place!
Damn you guys are smart!
No. Well, not really. More or less. Numbers are strings of bits in computing devices. These can be viewed as vectors, which are 1-dimensional matrices, but that view doesn’t give you anything. No interesting vector ops (like dot product) would be implemented inside of a calculator.
Matrices are heavily used in Computer Science, and not just for linear algebra reasons. All sorts of representations are encoded as matrices. From concrete networks to abstract data relations. Take a peek at Aho, Hopcroft and Ullman’s book on Algorithms.
Example: A network of computers. Number them from one to n. Build an nxn matrix: put a 1 at (i,j) if there is a link from computer i to computer j. Else put a zero. Perform what is known as a Boolean reflexive transitive closure on the marix. You now have a matrix that tells you what computers can talk to what other computers, directly or indirectly.
Not really. While I supposed you could make the argument that a binary word is just a single dimensional array of bits, the type of calculations that are done are not the typical matrix type of calculations. For example, when two numbers are added together, each bit is calculated by comparing the two input bits and producing two outputs, the actual data bit and a carry bit. The carry bit then goes into subsequent bit operations further on through the word. The simplest type of circuit to do this simply ripples the carry down through the logic gates, which is slow but effective.
There are very few machines which natively process arrays. Supercomputers and parallel processors are really good examples. Calculators and regular computers typically only do operations on two data elements at a time, so when an array is processed, it’s done by breaking up the processing into the individual elements. A pentium, for example, typically can only take two numbers from somewhere, do some operation on them, and store the result in a third place. Pentiums gain a little speed by having multiple execution pipelines (meaning that as long as the instructions don’t interfere with each other it can work on a couple of instructions at the same time), but this is nothing like the vector processing architecture of a cray for example.
While a pentium doesn’t handle matrices directly, matrix calculations (broken up into little bits for the CPU) are done all the time on pentiums. Three dimensional graphics are nothing more than a huge exercise in matrix math. Any game or 3 dimensional object displayed on your computer likely involes a lot of matrix manipulations. In fact, computer graphics are often taught as examples in linear algebra classes. Matrix translation and rotation are the main methods of translating bitmapped textures onto polygons (the basic building block of a 3 dimensional model), and a “normal vector” calculation is often used to determine whether a polygon is facing the “camera” so that the computer doesn’t waste time drawing polygons that aren’t visible.
Vectors are also used to calculate things like air flow around a vehicle, to make your car more aerodynamic and to figure out how a plane will fly, for example. One of the more famous things that the old cray supercomputer was used for was calculating the airflow around the space shuttle.
A few more applications of matrices off the top of my headL economics, statistics, making models of weather patterns, studying tornados and hurricanes, and modelling complex systems like power distribution.
It would probably be easier to list examples of fields where matrices aren’t used. They really are that important.
Hmm with all this talk of cross products etc, how can I resist …
Q: What do you get when you cross an elephant with a zebra?
A: Elephant zebra sine theta.
Q: What do you get when you cross an elephant with a mountain climber?
A: Nothing. The mountain climber is a scalar.
moejuck and zoid, it’s a common misconception that math is only for “smart people”. Sure, you have to think to do math. But “smart people” aren’t the only ones who can think, and thinking mathematically gets easier with practice. The only time you’re not smart enough to learn something is when you tell yourself you’re not smart enough to learn something.