Matrices as Linear Transformations
We all learned at an early age that in spite of the similarities, there is a significant difference between a left shoe and a right shoe. How does a mathematician recognize and describe this difference? To a mathematician, the right shoe is the reflection of the left shoe, and vice versa. Look in the mirror at a left shoe’s reflection next to its companion right shoe to see why. It turns out that the difference between some objects and their reflections can be substantial, even more so than for shoes!
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