Question about the matrix operation used in the slides

The picture below is a screenshot from the “Using per-item features” video from the “collaborative filtering” section.
I can’t seem to understand what matrix operation has been used here…

It looks like two 2x1 matrices (w^(1) and x^(3)) are multiplied and resulted in a single scalar value (4.95).

Multiplying matrices that are in the same shape is not correct mathematically. Also, the matrices are not square, so this can’t be the result of multiplying their determinant either, since determinant is not defined for non-square matrices.

I’m a bit lost here…

Edit: this operation is also used in the " Collaborative filtering algorithm" video.

Here, w^(1) times x^(1) resulted in 5. I would appreciate it if anyone could name this matrix operation.

Hi!

This operation is called the dot product.
See this wikipedia page here: Dot product - Wikipedia

1 Like

I see now!
Thank you very much!

it wasn’t a matrix operation after all! it was a vector operation.
It’s actually the vector dot product and I confused it with the matrix product.

The w^(1) and x^(1) were treated as vectors, not matrices. It all makes sense now!

If anyone else was confused about this too, here is a link for further reading: