added 20 characters in body

edited Feb 9, 2012 at 12:33

275.2k
34
606
1.5k

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11, F12, F13, 0, 0}, {F12, F22, 0, 0, 0}, {F13, 0, F33, 0,F35}, {0, 0, 0, F44, F45}, {0, 0, F35, F45, F55}}

Ftemp = {{F11, F12, F13, 0, 0}, {F12, F22, 0, 0, 0}, {F13, 0, F33, 0,F35}, {0, 0, 0, F44, F45}, {0, 0, F35, F45, F55}}

All the elements in the matrix real. We know there exists a positive square root for this matrix , however , it will be horrible analytically. What I would like to know however, is which entries in the resulting solution will be different from zero (and thus which entries will be zero).

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11, F12, F13, 0, 0}, {F12, F22, 0, 0, 0}, {F13, 0, F33, 0,F35}, {0, 0, 0, F44, F45}, {0, 0, F35, F45, F55}}

All the elements in the matrix real. We know there exists a positive square root for this matrix , however , it will be horrible analytically. What I would like to know however, is which entries in the resulting solution will be different from zero (and thus which entries will be zero).

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11, F12, F13, 0, 0}, {F12, F22, 0, 0, 0}, {F13, 0, F33, 0,F35}, {0, 0, 0, F44, F45}, {0, 0, F35, F45, F55}}

All the elements in the matrix real. We know there exists a positive square root for this matrix , however , it will be horrible analytically. What I would like to know however, is which entries in the resulting solution will be different from zero (and thus which entries will be zero).

deleted 195 characters in body

Source Link

edited Feb 9, 2012 at 11:47

PaulW

73
1
5

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11,F12,F13,0, 0 }, {F21,F22,0, F24,0 }, {0, 0, F33,0, F35}, {0, 0, 0, F44,F45}, {0, 0, F53,F54,F55}}; MatrixPower[Ftemp, 1/2] Out[1]= MatrixPower[(F11 F12 F13 0 0 F21 F22 0 F24 0 0 0 F33 0 F35 0 0 0 F44 F45 0 0 F53 F54 F55 ),1/2]

Why is this? AlsoFtemp = {{F11, is it possible to assignF12, F13, 0, 0}, {F12, F22, 0, 0, 0}, {F13, 0, F33, 0,F35}, {0, 0, 0, F44, F45}, {0, 0, F35, F45, F55}}

All the attributes ofelements in the matrix above so Mathematica knowsreal. We know there exists a positive square root for this matrix , however , it will be horrible analytically. What I would like to know however, is positive definite and could thus simplifywhich entries in the resulting diagonalisationsolution will be different from zero / square rooting?(and thus which entries will be zero).

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11,F12,F13,0, 0 }, {F21,F22,0, F24,0 }, {0, 0, F33,0, F35}, {0, 0, 0, F44,F45}, {0, 0, F53,F54,F55}}; MatrixPower[Ftemp, 1/2] Out[1]= MatrixPower[(F11 F12 F13 0 0 F21 F22 0 F24 0 0 0 F33 0 F35 0 0 0 F44 F45 0 0 F53 F54 F55 ),1/2]

Why is this? Also, is it possible to assign the attributes of the matrix above so Mathematica knows it is positive definite and could thus simplify the resulting diagonalisation / square rooting?

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11, F12, F13, 0, 0}, {F12, F22, 0, 0, 0}, {F13, 0, F33, 0,F35}, {0, 0, 0, F44, F45}, {0, 0, F35, F45, F55}}

All the elements in the matrix real. We know there exists a positive square root for this matrix , however , it will be horrible analytically. What I would like to know however, is which entries in the resulting solution will be different from zero (and thus which entries will be zero).

deleted 30 characters in body; edited tags; edited title

Source Link

edited Feb 8, 2012 at 15:16

rm -rf ♦

89.8k
21
303
498

Square rooting Obtaining the square-root of a general positive definite matrix

I have a mathematica question that i've tried quite hard without success to solve. I'm sure this has something to do with not using mathematica since 2001.

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = ASS = A) I'm trying :

In[1]= Ftemp = {{F11,F12,F13,0, 0 }, {F21,F22,0, F24,0 }, {0, 0, F33,0, F35}, {0, 0, 0, F44,F45}, {0, 0, F53,F54,F55}}; MatrixPower[Ftemp, 1/2] Out[1]= MatrixPower[(F11  F12 F13 0 0  F21 F22 0 F24 0  0 0 F33 0 F35  0 0 0 F44 F45  0 0 F53 F54 F55     ),1/2]

whyWhy is this? Also, is it possible to assign the attributes of the matrix above so mathematicaMathematica knows it is positive definite and could thus simplify the resulting diagonalisation / square rooting?

Square rooting a general positive definite matrix

I have a mathematica question that i've tried quite hard without success to solve. I'm sure this has something to do with not using mathematica since 2001.

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

In[1]= Ftemp = {{F11,F12,F13,0,0},{F21,F22,0,F24,0},{0,0,F33,0,F35},{0,0,0,F44,F45},{0,0,F53,F54,F55}}; MatrixPower[Ftemp, 1/2] Out[1]= MatrixPower[(F11  F12 F13 0 0 F21 F22 0 F24 0 0 0 F33 0 F35 0 0 0 F44 F45 0 0 F53 F54 F55   ),1/2]

why is this? Also, is it possible to assign the attributes of the matrix above so mathematica knows it is positive definite and could thus simplify the resulting diagonalisation / square rooting?

Obtaining the square-root of a general positive definite matrix

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., SS = A) I'm trying :

Ftemp = {{F11,F12,F13,0, 0 }, {F21,F22,0, F24,0 }, {0, 0, F33,0, F35}, {0, 0, 0, F44,F45}, {0, 0, F53,F54,F55}}; MatrixPower[Ftemp, 1/2] Out[1]= MatrixPower[(F11 F12 F13 0 0  F21 F22 0 F24 0  0 0 F33 0 F35  0 0 0 F44 F45  0 0 F53 F54 F55   ),1/2]

Why is this? Also, is it possible to assign the attributes of the matrix above so Mathematica knows it is positive definite and could thus simplify the resulting diagonalisation / square rooting?