= Covariance ellipse
{title2=$x^T\Sigma^{-1}x=1$}
For a two-dimensional <positive-definite> <covariance matrix> $\Sigma$, the centered <covariance ellipse> is the image of the <unit circle> under its positive definite <square root of a matrix>. Equivalently, it satisfies $x^T\Sigma^{-1}x=1$. Its <semi-major and semi-minor axes> have <lengths> given by the square roots of the larger and smaller <eigenvalues>, along the corresponding <eigenvectors>. The <ellipse> encodes a second-moment geometry; a probability-coverage interpretation needs additional information about the <probability distribution> and the chosen scale.
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