How this calculation works
Factor a symmetric positive definite matrix as LLᵀ.
THE FORMULA
L₁₁=√a, L₂₁=b/L₁₁, L₂₂=√(d−L₂₁²)A worked example
For [[4,2],[2,3]], the lower triangular entries are 2, 1 and √2.
Good to know
The matrix must be strictly positive definite.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Factor a symmetric positive definite matrix as LLᵀ.
The primary result is labeled “L₁₁”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The matrix must be strictly positive definite.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For [[4,2],[2,3]], the lower triangular entries are 2, 1 and √2.
Which rule does this calculator apply?
L₁₁=√a, L₂₁=b/L₁₁, L₂₂=√(d−L₂₁²)