Need clarification in single dimension matrix multiplication

[Anshul007]

Hi There,

I have always seen any coding language from the math's perspective. but I got one doubt in the video Learn PyTorch for deep learning in a day. Literally at 2:22:05

1. shape of the tensor

sample = torch.tensor([1,2,3],[4,5,6],[7,8,9])
sample.shape

output :
torch.Size([3, 3])

This is for me is this is matrix of size/shape is 3 by 3. i.e. 3 rows and 3 columns

2. Now matrix multiplication of 2 different matrix

one = torch.tensor([[8, 17, 21],
                    [9, 20, 12],
                    [16, 15, 23]])
two = torch.tensor([[14, 7, 22],
                    [10, 18, 19],
                     [25, 6, 11]])
torch.matmul(one,two)

output :

tensor([[807, 488, 730],
        [626, 495, 710],
        [949, 520, 890]])

The math behind is for [807 = 8*14 + 17*10 + 21*25]. same also explained in lecture How to Multiply Matrices
i.e. in math as well as in code, for any matrix multiplication if matrix one is 2 by 3 and matrix two is 3 by 4 then the resulted matrix will be 2 by 4. because this will take first row from left side matrix and first column from second matrix then do a multiply and store it in first place in the resulted matrix.

---

Final question
3. Then why multiplication for single dimension is different for code wise and math wise.

one = torch.tensor([5,1,2])
two = torch.tensor([3,0,4])
torch.matmul(one,two)

output:

tensor(23)

In Math
one(1by3) matmul two(1by3) is not possible. Cause, in-order to do multiplication rows from the left matrix has to be same as columns from the right matrix

Note: Let me know if I am not clear.

[sachinlodhi]

Okay let us start with the first part:
sample = torch.tensor([1,2,3],[4,5,6],[7,8,9]) sample.shape
It will throw syntax error as you are passing three lists as an arguments separated by comma.
The correct way to do it is:
sample = torch.tensor([[1,2,3],[4,5,6],[7,8,9]]) sample.shape
now it will be
torch.Size([3, 3])
Regarding your second question:
if both the tensors are 1D(as in your case) then it will return scaler value(23) in your case.
It is mentioned in the documentation here: https://pytorch.org/docs/stable/generated/torch.matmul.html#:~:text=The%20behavior%20depends,product%20is%20returned.