I am having a hard time understanding how matrix works.

a = [ 1 0; 2 1] ;
b= [ -1 2 ; 0 1] ;
n= a*b
N= a.*b

what is the mathematical differnce between a.*b and a*b.

Answer 1

[Jan]

.* is the elementwise multiplication, while * is the matrix multiplication:

[a,b; c,d] .* [e,f; g,h] = 
[a*e, b*f;  c*g, d*h]

[a,b; c,d] * [e,f; g,h] =     % [EDITED, typos fixed]
[a*e + b*g, a*f + b*h;  c*e + d*g, c*f + d*h]

See: https://en.wikipedia.org/wiki/Matrix_multiplication

[Caleb Banga]

Using this formula. I got -1,2,-2,1 but somehow matlab spit out -1,2,-2,5. I don’t understand how they are getting 5.

[Les Beckham]

@Jan - I think that you mean * instead of .* in your second example, right?

[Caleb Banga]

First example is with “.” And the second is without “.”

[Stephen23]

Corrected matrix multiplication formula:

[a,b; c,d] * [e,f; g,h] =

[a*e + b*g, a*f + b*h; c*e + d*g, c*f + d*h]

% ^ ^

Lets try both of them using the symbolic toolbox:

syms a b c d e f g h
[a,b; c,d] .* [e,f; g,h]

ans = 

[a,b; c,d] * [e,f; g,h]

ans = 

[Jan]

@Stephen: Thanks! I've tried to do it manually instead of letting Matlab do this with syms. I do not have the symbolic toolbox and it is beyond my understanding of fair use, that I can simply run it in the forum's online version.

I'm impressed, that you have checked this pile of characters, which are looking like small flies if you are looking from a distance of about 5 meters.

[Walter Roberson]

Jan, if the forum will run symbolic toolbox code for you then you are authorized to use the toolbox within the context of the forum; it is a service being provided by Mathworks.

It has the usual 55 second limit, and only about 5 gigabytes of ram, is about half the speed of your desktop, debugger and interactive input is disabled...

[Stephen23]

@Jan: my pleasure! I also spent ten minutes trying to catch those flies, going through the steps of multiplying: however I am slow and those tiny flies are hard to catch. It was only when I was about to post the comment that it occured to me to try the symbolic toolbox, which luckily gave the same result :)

Answer 2

[Walter Roberson]

The operator .* is element-by-element multiplication. N = a.*b means that N(J,K) = a(J,K) times b(J,K) with no other elements of a or b influencing the outcome.

The operator * is algebraic matrix multiplication, also known as "inner product". n = a*b means that n(J,K) = dot(a(J,:), b(:,K)) which is an operation that involves a complete row of one matrix and a complete column of the other matrix. Carefully chosen matrix multiplication can express rotation, translation, and scale

Answer 3

[Arthur Reis]

'*' is the matrix multiplication as is usual in Linear Algebra

'.*' is element-wise multiplication. Each element is multiplied by its correspondent