Tensor Contraction Calculator 2D To 8D

Tensor Contraction Calculator (2D to 8D) computes the contraction of two tensors over specified indices. Define tensor dimensions (2 to 8), sizes, contraction indices, and element values, then click “Calculate Contraction” to see the resulting tensor.

How to Use Tensor Contraction Calculator:

1. Enter the number of dimensions for Tensor A and Tensor B (2 to 8).
2. Specify sizes for each dimension.
3. Enter element values for both tensors.
4. Add contraction index pairs (e.g., index 1 of A with index 2 of B).
5. Select output format (array or matrix for 2D results).
6. Click “Calculate Contraction” to see the resulting tensor.
7. Use “Share Result” or “Copy Result” to share or copy the output.

Calculation Details:

The calculator performs tensor contraction:

• Tensor A: Defined by dimensions and sizes, e.g., \\( A_{i_1i_2\ldots} \\).
• Tensor B: Defined by dimensions and sizes, e.g., \\( B_{j_1j_2\ldots} \\).
• Contraction: Sum over specified indices, e.g., \\( C_{i_1i_2\ldots j_1j_2\ldots} = \sum_k A_{i_1i_2\ldots k} B_{k j_1j_2\ldots} \\).
• Result Tensor: Combines uncontracted indices with computed elements.

Note: Dimension sizes are limited to 5 to avoid excessive computation. Matrix output is only for 2D results.

Important Notes:

• Contraction indices must have matching sizes.
• At least one index pair is required for contraction.
• Large tensors (>10,000 elements) may slow down calculations.
• Clipboard access requires HTTPS. If copying fails, try accessing over HTTPS or copy manually.