Data Analysis Write a Porgram

How to write a program for finding the ortogonal projection of a given vector V1 on another given vector V2??

How should ı do? Which Matlab commands should i use?

[Jan]

How would you do this with pencil and paper?

[John D'Errico]

Jan's question is the perfect one: I.e., How would you do it on paper, as if you know how to do that, then you can trivially write the MATLAB code. If you don't understand that, then this is surely a homework problem for you, and you need to make an effort.

[Mustafa Furkan SAHIN]

I know orthogonal projection is done like this, but I have no idea how to write this in matlab. If I define Vector V1 and V2, multiply as V1.*V2 then divide to V1.^2. Then multiply the result from here by Vector 1. Will i get correct results?

[Jan]

V1 .* V2 is the elementwise multiplication. You want the dot product instead: V1 * V2.' or dot(V1, V2). Mathematically this can be expressed as sum(V1 .* V2) also.

V1 .^ 2 squares each element, but you want the norm of the vectors: norm(V2)^2. This can be written as sum(V1 .* V1) also.

Try it. There are some different possible commands only, so you can solve this by "gunshot programming": modify the code until the result is as expected.

[Mustafa Furkan SAHIN]

V1 = input('Vector V1= ');

V2 = input('Vector V2= ');

frstprt= dot(V1,V2)/norm(V1,2)^2;

scndprt = frstprt.*V1;

I got the correct result with this Matlab program.Thank you very much for helping me understand the matlab code.

Answer 1

[Mustafa Furkan SAHIN]

V1 = input('Vector V1= ');
V2 = input('Vector V2= ');
frstprt= dot(V1,V2)/norm(V1,2)^2;
scndprt = frstprt.*V1;