Orthogonal matrix

Imagine you have a big puzzle and you want to move the pieces around, but you don't want to change the shape or size of the puzzle. An orthogonal matrix is like a special tool that you can use to move the puzzle pieces around in a certain way, without changing the overall shape and size of the puzzle.

To make it simpler, let's say you have a shape made of blocks that you want to move around. An orthogonal matrix is a tool that you can use to move those blocks, but only in certain ways - like rotating them or flipping them over - and still keep the same basic shape.

The matrix itself is like a grid that you put over the shape of the blocks. Each row and column of the matrix represents a different direction that you can move the blocks in. And the numbers in the matrix tell you how much to move the blocks in each direction.

But because it's orthogonal, it means that all the directions in the matrix are at right angles to each other - like the corners of a square. This makes it easier to move the blocks around without changing their overall shape.

So in short, an orthogonal matrix is like a special tool that you can use to move shapes around without changing their basic shape or size. It's like a set of instructions that keep everything in the right place, no matter how you move it.