คูณเมทริกซ์ด้วย matmul และ @

Multiplying tensors with the star sign is elementwise. Matrix multiplication is different: it mixes rows and columns into weighted sums.

Each output entry of a matrix multiply is a dot product: one row of the left matrix paired with one column of the right matrix.

To multiply shapes (m, k) and (k, n), the inner k must agree. The result is (m, n): outer dimensions survive, the inner one is summed away.

Python gives matrix multiply its own clean symbol. The @ operator multiplies two tensors the matrix way, no loops in sight.

torch.matmul is the spelled-out twin of @. Same result, handy when you prefer a named function call in your code.

A (2, 3) times a (3, 4) gives a (2, 4). Read the shapes left to right and the inner 3 cancels, leaving the outer pair.

Do not confuse them: a * b is elementwise and needs matching shapes, while a @ b is matrix multiply and needs matching inner dimensions.

Multiply a matrix by a 1D vector and you get a vector. Each output number is the dot product of a matrix row with that vector.

matmul handles batches: feed shapes (B, m, k) and (B, k, n) and it multiplies each of the B matrix pairs at once, returning (B, m, n).

Mismatch the inner dimensions and PyTorch throws a clear RuntimeError. Reading those shape messages quickly becomes your fastest debugging tool.

This one operation is everywhere. A linear layer is just inputs times a weight matrix plus a bias, and matmul does that heavy lifting.

Time to check your shape arithmetic.

Matrix multiply with @ or torch.matmul pairs rows with columns into dot products; inner dimensions must match, outer ones survive. It powers every layer. 🔗