Hello. I'd like to solve this problem by Python. Implement modified Gram-Schmidt QR-factorization. Write a function which given an A ∈ C m×n computes Q ∈ C m×n , and R ∈ C n×n — qr mgs(A) → Q, R. Work through experiment of Trefethen & Bau. Note that depending on your coding environment, you may have to use larger (and worse conditioned) matrices to achieve the loss of orthogonality in classical Gram-Schmidt

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.