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Optimal projection equations are mathematical formulations used in various fields, particularly in optimization and data analysis, to find the best representation of data in a reduced-dimensional space. These equations help to project high-dimensional data onto a lower-dimensional space while preserving essential characteristics of the data. ### Key Concepts 1. **Projection**: In a mathematical and geometrical sense, projection refers to mapping points from a higher-dimensional space to a lower-dimensional space. This is often done through linear transformations.

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  1. Control theory
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