Cholesky Decomposition

Updated 01 Oct 2026

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What it is
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  factors a real symmetric positive-definite matrix as $A=LL^T$
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Use
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  solve $Ly=b$ , then $L^Tx=y$ .
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  3exploits symmetry and positive definiteness to use less work and storage than general LU.
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Requirements
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  symmetry alone is insufficient; positive definiteness is essential for the standard real Cholesky factorization
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related
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  System of Linear Equations
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  Conjugate Gradient Method
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s

Linked references 3