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PRB147
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If one [tex]4\times 4[/tex] matrix have two vanishing eigenvalues, does the matrix have a square root?
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That's not true. There are many non-diagonalizable matrices that have square roots, e.g.transgalactic said:in order to make a squere root of a matrix you need to build first a digonizable form of the given matrix
The square root of a matrix is another matrix that, when multiplied by itself, results in the original matrix.
No, not all matrices have a square root. A matrix must have all real, non-negative eigenvalues to have a square root.
The square root of a matrix can be calculated using diagonalization or the Jordan canonical form.
The principal square root of a matrix is the unique matrix with all positive eigenvalues, while non-principal square roots may have negative eigenvalues.
The square root of a matrix is used in various fields such as physics, engineering, and computer science to solve systems of equations, simulate processes, and analyze data.