Tensor Contraction Calculator (2D)

Description

This Tensor Contraction Calculator computes the contraction of two 2D tensors over specified indices, displaying results and steps for analysis.

Tensor 1 (e.g., [[1,2],[3,4]]): Tensor 2 (e.g., [[5,6],[7,8]]): Contraction Indices (e.g., 1,0):

For tensors A[i,k] and B[k,j], the contraction over index k computes:

C[i,j] = Σ_k (A[i,k] * B[k,j])

Where i and j are free indices, and k is the summed (dummy) index, reducing the tensor rank by 2.

Example 1: Tensor 1: [[1,2],[3,4]], Tensor 2: [[5,6],[7,8]], Indices: 1,0
Solution: [[19,22],[43,50]]
Example 2: Tensor 1: [[1,0],[0,1]], Tensor 2: [[1,2],[3,4]], Indices: 1,0
Solution: [[1,2],[3,4]]
Example 3: Tensor 1: [[2,2],[2,2]], Tensor 2: [[1,1],[1,1]], Indices: 1,0
Solution: [[4,4],[4,4]]
Example 4: Tensor 1: [[0,1],[1,0]], Tensor 2: [[1,0],[0,1]], Indices: 1,0
Solution: [[0,1],[1,0]]
Example 5: Tensor 1: [[1,2,3],[4,5,6]], Tensor 2: [[7,8],[9,10],[11,12]], Indices: 1,0
Solution: [[58,64],[139,154]]