Published On Feb 22, 2024
A positive-definite matrix is a (real) symmetric matrix with all its eigenvalues being positive. Such a matrix induces a new kind of inner product, the positive-definite inner product, which induces a new norm.
Using this inner product and the norm, we can derive the familiar Cauchy-Schwarz and triangle inequalities. We briefly discuss the connection between the positive-definite matrix and the kernel method.
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