How can you stretch or squash a square without changing its shape?
Image: Maxibu, CC BY-SA 4.0, via Wikimedia Commons
orthogonal matrices preserve distances: O^T O = I means no stretching or squashing
How can you stretch or squash a square without changing its shape?
Imagine you have a square piece of paper. You want to fold it in a way that it still looks like a square but might look stretched or squashed.
Think of the square paper as a grid. If you rotate it perfectly, the grid lines stay straight and evenly spaced. This perfect rotation keeps the square's shape intact.
Example
Rotating a 2x2 square by 90 degrees keeps it a 2x2 square.
Remember this
Rotating an orthogonal matrix by 90 degrees doesn't change its shape, preserving distances.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
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