Linear Algebra

Spectral Decomposition (Symmetric Matrices)

Decompose a symmetric matrix as A = QΛQᵀ = Σ λᵢ qᵢqᵢᵀ — a sum of rank-1 outer products.

Settings
Matrix A
Matrix is not symmetric. Enable auto-symmetrize or enter a symmetric matrix.

Eigenvalues (Spectral Values)

Enter a symmetric matrix and click Compute.

Q, Λ, and Outer Product Terms

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Rank-1 Terms and Their Sum

Step-by-Step Solution

Steps will appear here after computing.