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edit approved Feb 13, 2017 at 9:05
Amir Sagiv
edit approved Feb 13, 2017 at 9:05
Amir Sagiv
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maximum Maximum eigenvalue of hadamardHadamard power of a positive semidefinite matrix

Let K$K$ be a covariance matrix (it. It is positive semidefinite, it'sits diagonal elements are all 1, and it'sits off-diagonals are between -1 and 1). Let K.^2$K.^2$ be its element-wise power (Hadamard power). Can we show that maximum eigenvalue of K>=$K$ are great or equal than the maximum eigenvalue of K.^2$K.^2$? K can have both positive and negative elements.

maximum eigenvalue of hadamard power of a positive semidefinite matrix

Let K be a covariance matrix (it is positive semidefinite, it's diagonal elements are all 1, and it's off-diagonals are between -1 and 1). Let K.^2 be its element-wise power (Hadamard power). Can we show that maximum eigenvalue of K>= maximum eigenvalue of K.^2? K can have both positive and negative elements.

Maximum eigenvalue of Hadamard power of a positive semidefinite matrix

Let $K$ be a covariance matrix. It is positive semidefinite, its diagonal elements are all 1, and its off-diagonals are between -1 and 1. Let $K.^2$ be its element-wise power (Hadamard power). Can we show that maximum eigenvalue of $K$ are great or equal than the maximum eigenvalue of $K.^2$?

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Soheil Feizi
Soheil Feizi
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maximum eigenvalue of hadamard power of a positive semidefinite matrix

Let K be a covariance matrix (it is positive semidefinite, it's diagonal elements are all 1, and it's off-diagonals are between -1 and 1). Let K.^2 be its element-wise power (Hadamard power). Can we show that maximum eigenvalue of K>= maximum eigenvalue of K.^2? K can have both positive and negative elements.