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## Main Question or Discussion Point

Matlab help state that the square root of [tex]X = \begin{pmatrix} 7 & 10 \\ 15 & 22 \end{pmatrix}[/tex]

are

[tex]A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}[/tex] , [tex]B = \begin{pmatrix} 1.5667 & 1.7408 \\ 2.6112 & 4.1779 \end{pmatrix}[/tex]

, C=-A and D=-B .

When I used the matlab command expm(0.5*logm(X)) to compute the square root of X, I obtained the matrix B.

My questions:

1. Does it make sense to define the nth root for any given square matrix X ?

2. If it does, in general how many A are there such that A

3. If I am to use the command expm(logm(X)/n) to compute [itex]\sqrt[n]{X}[/itex] which answer will I get.

are

[tex]A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}[/tex] , [tex]B = \begin{pmatrix} 1.5667 & 1.7408 \\ 2.6112 & 4.1779 \end{pmatrix}[/tex]

, C=-A and D=-B .

When I used the matlab command expm(0.5*logm(X)) to compute the square root of X, I obtained the matrix B.

My questions:

1. Does it make sense to define the nth root for any given square matrix X ?

2. If it does, in general how many A are there such that A

^{n}=X ?3. If I am to use the command expm(logm(X)/n) to compute [itex]\sqrt[n]{X}[/itex] which answer will I get.