2.II.14E
(a) Let be an positive-definite, symmetric matrix. Define the Cholesky factorization of and prove that it is unique.
(b) Let be an matrix, , such that . Prove the uniqueness of the "skinny QR factorization"
where the matrix is with orthonormal columns, while is an upper-triangular matrix with positive diagonal elements.
[Hint: Show that you may choose as a matrix that features in the Cholesky factorization of .]
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