# Linear Algebra Calculators

## Cholesky Factorization

This calculator uses Wedderburn rank reduction to find the Cholesky factorization of a symmetric positive definite matrix $A$. The process constructs the matrix $L$ in stages.

At each stage you'll have an equation $A=LL^T+B$ where you start with $L$ nonexistent and with $B=A$. The next column of $L$ is chosen from $B$. (The $L$ column is scaled.) Then $L$ and $B=A-LL^T$ are updated. Eventually $B=0$ and $A=LL^T$.

At this point $L$ is lower triangular. If the original matrix $A$ wasn't positive definite, the algorithm will fail at some point when confronted with the square root of a negative quantity.

Either choose a size and press this button to get a randomly generated matrix, or enter your matrix in the box below. (Look at the example to see the format.)

Matrix $A$:

Update $L$ and $B$.

The reset button leaves the $A$ matrix alone, but reinitializes $L$ and $B$.

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