Invariants of tensors

How can you predict the future?

Imagine you're playing a game where you roll a dice to move forward on a board. You want to know if there's a pattern to winning.

Think of the board as a 3x3 matrix. The game's rules can change the matrix, and the winning positions are like the matrix's eigenvalues. These eigenvalues tell us the outcomes of applying the game's rules repeatedly.

Example

If the matrix is [[2, 0, 0], [0, 3, 0], [0, 0, 4]], the eigenvalues are 2, 3, and 4, showing stable positions on the board.

Remember this

Eigenvalues predict stable outcomes in repeated applications of a matrix.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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