Geodesic
On a Factorisation of Positive Definite Matrices
Canadian mathematical bulletin, Tome 6 (1963) no. 3, pp. 405-407

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All our matrices are square with real elements. The Schur product of two n × n matrices B = (bij) and C = (cij) (i, j, = 1, 2, ..., n), is an n × n matrix A = (aij) with aij = bij cij, (i, j = 1, 2, ..., n).A result due to Schur [1] states that if B and C are symmetric positive definite matrices then so is their Schur product A. A question now a rises. Can any symmetric positive definite matrix be expressed as a Schur product of two symmetric positive definite matrices? The answer is in the affirmative as we show in the following theorem. 
Majindar, Kulendra N. On a Factorisation of Positive Definite Matrices. Canadian mathematical bulletin, Tome 6 (1963) no. 3, pp. 405-407. doi: 10.4153/CMB-1963-035-9
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     title = {On a {Factorisation} of {Positive} {Definite} {Matrices}},
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     doi = {10.4153/CMB-1963-035-9},
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