Multiplying Vectors by a Matrix Entry-wise

[jemma]

Hi, this is probably a really simple problem but I'm trying to multiply vectors by a matrix, using entry-wise multiplication.
For example, I want to do something like this:

a = [1 2 3 4]
b = [5 6 7 8]'
c = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16]

d = a.*b.*c

So that d is a 4x4 matrix and for example:

d(1,2) = 1*5*1 (etc.) So that each entry in the first row of d will be multiplied by b(1) and the corresponding a entry. Does this make sense? Anyway, is this possible?

Thanks!

 

[mikeph]

To use entry-wise multiplication the matrix dimensions must be the same, which they are not. a.*b is a 1x4 matrix and c is a 4x4 matrix.
I don't understand your second to last line because you seem to be explaining how to find d(1,2) by describing an operation on d itself.

 

[jemma]

Sorry, I meant to say, for example,
d(1,1) = a(1) .* b(1) .* c(1)
and,
d(1,2) = a(2) .* b(1) .* c(2)

I basically want to multiply each entry of every row of 'c' by 'b' then each entry of every column of 'c' by 'a'.
So isn't this possible since the dimentions are different?

I guess just making
a=[1 2 3 4; 1 2 3 4; 1 2 3 4; 1 2 3 4]
and
b=[5 6 7 8; 5 6 7 8; 5 6 7 8; 5 6 7 8]'
Then d = a.*b.*c works OK.

 

[matonski]

a = [1 2 3 4]
b = [5 6 7 8]'
c = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16]
b*a.*c

 

[blue_raver22]

Hello, this is a great question and it is definitely possible to multiply vectors by a matrix using entry-wise multiplication. This type of multiplication is also known as the Hadamard product and it is a common operation in linear algebra. In your example, you are correctly using the dot product operator (.*), which multiplies each entry in the first row of matrix c by the corresponding entries in vectors a and b. This will result in a 4x4 matrix d, where each entry is the product of the corresponding entries in a, b, and c. This is a useful operation in many applications, such as image processing and signal processing, where you want to apply a transformation to each element in a matrix or vector. It is important to note that entry-wise multiplication is different from matrix multiplication, where the dimensions of the matrices must be compatible. I hope this helps clarify your question and good luck with your project!