Tensor diagram notation

Imagine you have a bunch of toy blocks with different colors and shapes. Each block can represent something different, like a number, a direction, or a vector. When we want to show how these blocks relate to each other, we can use a diagram that looks like a bunch of lines connecting the blocks.

This kind of diagram is called a tensor diagram, and it helps us understand how these blocks work together to do things like calculate forces or solve equations. The lines connecting the blocks represent how they are related to each other. For example, if two blocks are connected by a line, it means they are multiplied together. If a line connects one block to two others, it means the block is used to calculate a sum or difference between the other two blocks.

In tensor diagram notation, we use special symbols to represent these relationships between the blocks. For example, a dot in the middle of a line represents multiplication, while a line that splits into two at the end represents a sum or difference. By using these symbols, we can write down complex equations and calculations in a way that is easy to understand and visualize.

Overall, tensor diagram notation is like playing with toy blocks, but with a special language that helps us communicate complex ideas in a clear and simple way.