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  • https://math.libretexts.org/Bookshelves/Linear_Algebra/Linear_Algebra_with_Applications_(Nicholson)/08%3A_Orthogonality/8.03%3A_Positive_Definite_Matrices
    If A is any n×n matrix, let (r)A denote the r×r submatrix in the upper left corner of A; that is, (r)A is the matrix obtained from A by deleting the las...If A is any n×n matrix, let (r)A denote the r×r submatrix in the upper left corner of A; that is, (r)A is the matrix obtained from A by deleting the last nr rows and columns. UTU=(UT1D12)(D12U1)=UT1(D22)1U1=(UT1D11)U1=(L11)U1=A

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