Tensor contraction

Imagine you have some LEGO blocks that are all different sizes and shapes. Some are long, some are short, some are skinny, some are fat. Now let's say you want to combine some of these blocks together to make a bigger block. You might take a long block and attach it to a short block, and then attach a skinny block to the other end of the short block. This is kind of like what tensor contraction does - it takes different pieces (tensors) and combines them together in a certain way to create a bigger tensor.

But unlike LEGO blocks, tensors have different dimensions that need to match up for the contraction to work. If you have a 3x4 tensor and a 4x5 tensor, you can contract them along the middle dimension (the 4) to create a new 3x5 tensor. It's kind of like taking two trains that are the same length but have different types of cargo and combining them into one longer train with both types of cargo.

There are different ways you can contract tensors - some involve more complicated math and indexing, but the basic idea is the same. You take two or more tensors, find a matching dimension to contract along, and then perform some kind of multiplication or summation to create a new tensor with fewer dimensions. It's a way of simplifying complex data sets so that you can perform calculations or analysis on them more easily.