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Moving information about the problem from the comment section to the question itself. Added tag.
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Symmetric linear least squares-squares solution

Given an overdetermined linear system $AX=Y$ with knowntall matrices $A$ and $Y$, and the following overdetermined linear system in square matrix $X$

$$AX=Y$$

is there an explicit formula for the least squares-squares solution if $X$ is constrained to be symmetric ($X=X^T$)?

Symmetric linear least squares solution

Given an overdetermined linear system $AX=Y$ with known $A$ and $Y$, is there an explicit formula for the least squares solution if $X$ is constrained to be symmetric ($X=X^T$)?

Symmetric linear least-squares solution

Given tall matrices $A$ and $Y$ and the following overdetermined linear system in square matrix $X$

$$AX=Y$$

is there an explicit formula for the least-squares solution if $X$ is constrained to be symmetric?

removed clause about moore-penrose pseudoinverse
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Museful
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Given an overdetermined linear system $AX=Y$ with known $A$ and $Y$, the least-squares solution for $X$ is given by $X=A^+Y$ (where $A^+$ is the Moore-Penrose pseudoinverse of $A$).

But is there an explicit solutionformula for the least squares solution if $X$ is constrained to be symmetric ($X=X^T$)?

Given an overdetermined linear system $AX=Y$ with known $A$ and $Y$, the least-squares solution for $X$ is given by $X=A^+Y$ (where $A^+$ is the Moore-Penrose pseudoinverse of $A$).

But is there an explicit solution for the least squares solution if $X$ is constrained to be symmetric ($X=X^T$)?

Given an overdetermined linear system $AX=Y$ with known $A$ and $Y$, is there an explicit formula for the least squares solution if $X$ is constrained to be symmetric ($X=X^T$)?

Source Link
Museful
  • 223
  • 3
  • 7

Symmetric linear least squares solution

Given an overdetermined linear system $AX=Y$ with known $A$ and $Y$, the least-squares solution for $X$ is given by $X=A^+Y$ (where $A^+$ is the Moore-Penrose pseudoinverse of $A$).

But is there an explicit solution for the least squares solution if $X$ is constrained to be symmetric ($X=X^T$)?