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使用 matmul 和 @ 进行矩阵乘法

理解每一层背后的点积

使用 matmul 和 @ 进行矩阵乘法 是 CoddyKit 上的免费 Deep Learning Academy 课时。这是第 3 节课，共 4 节。你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。这是 Deep Learning Academy 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 Deep Learning Academy 课程共包含 4 节课。

本课时的部分内容尚未翻译，以英文显示。

Beyond Elementwise

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

Dot Products in Bulk

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.

The Inner Dimensions Must Match

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.

The @ Operator

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

c = a @ b

torch.matmul Does the Same

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

c = torch.matmul(a, b)

Mind the Shapes

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.

a = torch.randn(2, 3)
b = torch.randn(3, 4)
c = a @ b  # shape (2, 4)

Star Is Not At

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

Matrix Times Vector

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.

y = W @ x  # W is (n, m), x is (m,), y is (n,)

Batched matmul

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).

out = torch.matmul(batch_a, batch_b)

Shape Errors Are Loud

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

The Engine of Every Layer

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

out = x @ W.T + bias

Quick Check

Time to check your shape arithmetic.

Recap: Rows Meet Columns

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

常见问题解答

「使用 matmul 和 @ 进行矩阵乘法」课时是免费的吗？

是的 — 「使用 matmul 和 @ 进行矩阵乘法」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 Deep Learning Academy 课程的其余内容，请升级到 CoddyKit PRO。 Deep Learning Academy 课程共包含 4 节课。

「使用 matmul 和 @ 进行矩阵乘法」这节课中我会学到什么？

理解每一层背后的点积你通过在浏览器中直接运行的动手代码来练习 Deep Learning Academy，全天候 AI 导师会在你学习这节课的过程中回答你的问题。

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「使用 matmul 和 @ 进行矩阵乘法」课时需要多长时间？

大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。

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