Multiplying elements of a matrix and its transpose row-wise

I am a novice in Matlab. I have a variable U of the class 'double' and size 500 2 (so it corresponds to a 500x2 matrix). Each row corresponds to a vector so in reality I have 500 vectors. I want to take the dot product of each vector with itself and add the results:

result = U(1)'*U(1) + U(2)'*U(2) + ... + U(500)'*U(500)

I cannot figure out how to do this.

EDIT:

For example, if U = [1 2; 3 4] then I can define result1 = dot(U(1,:)',U(1,:)) and result2 = dot(A(2,:)',A(2,:))

Then I need to do result1 + result2. So I need to store the dot product of each row of U with it self to a list and then add the elements of the list.

Unfortunately I cannot make the following loop work:

for i = 1:length(A)

result1 = dot(A(i,:)',A(i,:))

end

ANSWER:

y = 0;

for n = 1:length(U)

y = y + dot(A(U,:)',A(U,:))

end

[Matt J]

Each row corresponds to a vector so in reality I have 500 vectors

result = U(1)'*U(1) + U(2)'*U(2) + ... + U(500)'*U(500)

Your terminology clashes confusingly with your formulas. Given a 1x2 row vector U, the expression U'*U yields a 2x2 result called the outer product, not the dot product. The dot product would be U*U' which gives a scalar.

[Gorbz]

I thought I used the standard * multiplication symbol that yields the dot product.

[Matt J]

No, the * multiplication symbol in Matlab means matrix multiplication and U' means the conjugate tranpose of U. Is your intended product operation supposed to produce a 2x2 output or something else?

Answer 1

[KSSV]

iwant = sum(A.*A) ;

where A is your 500*2 matrix.

[Gorbz]

The result of this is a 2d vector I am afraid.

[Stephen23]

sum(A.*A,'all')

Answer 2

[Matt J]

result=A.'*A;