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    4 QR Factorization 4.1 Reduced vs. Full QR Consider A ∈ Cm×n with m ≥ n. The reduced QR factorization of A is of the form A = QˆR,ˆ where Qˆ ∈ Cm×n with orthonormal columns and Rˆ ∈ Cn×n an upper triangular matrix

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    In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition: p. 38

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    for all indices and .. Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.

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    4 QR Factorization - Applied mathematics

    4 QR Factorization 4.1 Reduced vs. Full QR Consider A ∈ Cm×n with m ≥ n. The reduced QR factorization of A is of the form A = QˆR,ˆ where Qˆ ∈ Cm×n with orthonormal columns and Rˆ ∈ Cn×n an upper triangular matrix

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    B (n, p) Binomial distribution with parameters n and p Discrete probability distribution for the probability of number of successes in n independent random trials under the identical conditions. If X follows B (n, p) then, P (X = r) = r n r r n C (1 p ) , Where, 0 < p <1, r = 0,1,2, ...n Binomial Distribution c Confidence level c P( z

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    Suppose the n x k matrix A has QR factorization A = QR. We define the n x i matrices, Ai [a1a for i 1,...,k. Define the i x i matrix Ri as the sub matrix of R containing its first i rows and columns, for i = 1, k.

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    B (n, p) Binomial distribution with parameters n and p Discrete probability distribution for the probability of number of successes in n independent random trials under the identical conditions. If X follows B (n, p) then, P (X = r) = r n r r n C (1 p ) , Where, 0 < p <1, r = 0,1,2, ...n Binomial Distribution c Confidence level c P( z

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    6. The set Sym(X) of one to one and onto functions on the n-element set X, with multiplication defined to be composition of functions. (The elements of Sym(X) are called permutations and Sym(X) is called the symmetric group on X. This group will be discussed in more detail later. If α,∈Sym(X), then we define the image of xunder αto be xα ...

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    I Cn is the set of n-column vectors with components in C and similarly Cn n is the set of n n matrices with complex numbers as its entries. I We write the complex conjugate of z as z = x iy. For u 2Cn and A 2Cn n, we denote by u 2Cn and A 2Cn n, their complex conjugates, obtained by taking the complex conjugate of each of their components.

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