QR decomposition

description

• to decompose (phân tích) matrix A into 2 constituent matrices (2 ma trận thành phần) Q and R, $A=Q.R$
• basically, nothing else than the gram-schmidt orthogonalization process
  • A: square + invertible matrix
  • Q: orthogonal matrix, with $Q^T=Q^{-1}$ ⇒ columns of Q form orthonormal basis
  • R: upper triangular matrix (all entries below the main diagonal are zero)
  • see here
• find the orthonormal basis using gram-schmidt process → find Q and R
  • $Q=[e_1\cdots e_n]$
  • R as below
    •