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Matrix Multiplication with Einsum

Problem Statement

Use torch.einsum to perform matrix multiplication.

Background

Einstein summation (einsum) is a compact notation for tensor operations. The key idea is that repeated indices are summed over, while indices that appear in the output are preserved.

Your Task

The starter code creates matrices A (2x3) and B (3x2). Use torch.einsum to compute the matrix product of A and B.

The verification against torch.matmul is pre-filled.

Output Format

Returns a dictionary with "result", "shape", and "matches_matmul".

Example:

Input:

None

Output:

{'result': [[58.0, 64.0], [139.0, 154.0]], 'shape': [2, 2], 'matches_matmul': True}

Reasoning:

We create matrix A = [[1, 2, 3], [4, 5, 6]] and matrix B = [[7, 8], [9, 10], [11, 12]].
We compute C = A @ B using torch.einsum('ij,jk->ik', A, B), which performs matrix multiplication by summing over the shared index j: $C_{ik} = \sum_{j} A_{ij} B_{jk}$ .
The resulting matrix C is computed as: $C = \begin{bmatrix} 1*7+2*9+3*11 & 1*8+2*10+3*12 \\ 4*7+5*9+6*11 & 4*8+5*10+6*12 \end{bmatrix} = \begin{bmatrix} 58 & 64 \\ 139 & 154 \end{bmatrix}$ .
We verify the result by comparing it with torch.matmul(A, B), which yields the same result, so "matches_matmul" is True.

Constraints:

Use torch.einsum with 'ij,jk->ik'
Verify against torch.matmul
Return as nested list

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.