Let us refer to $D$ as the matrix with $D_{ij} = ||x_i - x_j||_2$ and $H = D \circ D$ e.g. the matrix with $H_{ij} = ||x_i - x_j||_2^2$ as its entries. Are the spectra of these matrices related at all? I suppose this question could be stated more generally in terms of Hadamard products.

In many papers, such as this one, $H$ is called a Euclidean Distance Matrices (EDM). Why? This matrix contains squared distances, not distances.

It seems that $H$ is more interesting to study for many reasons, such as the relationship between PCA and MDS. It is also clear that $H$ has been studied quite thoroughly.

This unaccepted answer is the only thing I can find which appears to relate these matrices, but, I am skeptical that it is correct. In particular, I believe when they write $D^2$ they mean $H$. If it is not a mistake, can someone clarify the definition of the matrix J? Unfortunately I cannot comment on the thread to ask this since I do not have enough reputation.

Let us refer to $D$ as the matrix with $D_{ij} = ||x_i - x_j||_2$ and $H = D \circ D$ e.g. the matrix with $H_{ij} = ||x_i - x_j||_2^2$ as its entries. Are the spectra of these matrices related at all? I suppose this question could be stated more generally in terms of Hadamard products.

In many papers, such as this one, $H$ is called a Euclidean Distance Matrices (EDM). Why? This matrix contains squared distances, not distances.

It seems that $H$ is more interesting to study for many reasons, such as the relationship between PCA and MDS. It is also clear that $H$ has been studied quite thoroughly.

This unaccepted answer is the only thing I can find which appears to relate these matrices, but, I am skeptical that it is correct. In particular, I believe when they write $D^2$ they mean $H$. If it is not a mistake, can someone clarify the definition of the matrix J? Unfortunately I cannot comment on the thread to ask this since I do not have enough reputation.

Let us refer to $D$ as the matrix with $D_{ij} = ||x_i - x_j||_2$ and $H = D \circ D$ e.g. the matrix with $H_{ij} = ||x_i - x_j||_2^2$ as its entries. Are the spectra of these matrices related at all? I suppose this question could be stated more generally in terms of Hadamard products.

In many papers, such as this one, $H$ is called an Euclidean Distance Matrices (EDM). Why? This matrix contains squared distances, non distances.

It seems that $H$ is more interesting to study for many reasons, such as the relationship between PCA and MDS. It is also clear that $H$ has been studied quite thoroughly.

This unaccepted answer is the only thing I can find which appears to relate these matrices, but, I am skeptical that it is correct. In particular, I believe when they write $D^2$ they mean $H$. If it is not a mistake, can someone clarify the definition of the matrix J? Unfortunately I cannot comment on the thread to ask this since I do not have enough reputation.

Let us refer to $D$ as the matrix with $D_{ij} = ||x_i - x_j||_2$ and $H = D \circ D$ e.g. the matrix with $H_{ij} = ||x_i - x_j||_2^2$ as its entries. Are the spectra of these matrices related at all? I suppose this question could be stated more generally in terms of Hadamard products.

In many papers, such as this one, $H$ is called a Euclidean Distance Matrices (EDM). Why? This matrix contains squared distances, not distances.

It seems that $H$ is more interesting to study for many reasons, such as the relationship between PCA and MDS. It is also clear that $H$ has been studied quite thoroughly.

This unaccepted answer is the only thing I can find which appears to relate these matrices, but, I am skeptical that it is correct. In particular, I believe when they write $D^2$ they mean $H$. If it is not a mistake, can someone clarify the definition of the matrix J? Unfortunately I cannot comment on the thread to ask this since I do not have enough reputation.

In many papers, such as this one Euclidean Distance Matrices (EDM's) are referred to as it's Hadamard square. Why? This matrix is not the euclidean distance matrix.

Lets refer to $D$ as the matrix with $D_{ij} = ||x_i - x_j||_2$ and $H = D \circ D$ e.g. the matrix with $H_{ij} = ||x_i - x_j||_2^2$ as its entries. Are the spectrums of these matrices related at all? I suppose this question could be stated more generally in terms of hadamard products.

It seems that $H$ is more interesting to study for many reasons, such as the relationship between PCA and MDS. It is also clear that $H$ has been studied quite thoroughly.

This unaccepted answer is the only thing I can find which appears to relate these matrices, but, I am skeptical that it is correct. In particular, I believe when they write $D^2$ they mean $H$. If it is not a mistake, can someone clarify the definition of the matrix J? Unfortunately I cannot comment on the thread to ask this since I do not have enough reputation.

Let us refer to $D$ as the matrix with $D_{ij} = ||x_i - x_j||_2$ and $H = D \circ D$ e.g. the matrix with $H_{ij} = ||x_i - x_j||_2^2$ as its entries. Are the spectra of these matrices related at all? I suppose this question could be stated more generally in terms of Hadamard products.

In many papers, such as this one, $H$ is called an Euclidean Distance Matrices (EDM). Why? This matrix contains squared distances, non distances.

It seems that $H$ is more interesting to study for many reasons, such as the relationship between PCA and MDS. It is also clear that $H$ has been studied quite thoroughly.

This unaccepted answer is the only thing I can find which appears to relate these matrices, but, I am skeptical that it is correct. In particular, I believe when they write $D^2$ they mean $H$. If it is not a mistake, can someone clarify the definition of the matrix J? Unfortunately I cannot comment on the thread to ask this since I do not have enough reputation.