Text S2 - PLoS ONE
... We define C as the n n matrix of three-leg travel probabilities, with the ij th element equal to l , k Ail Blk C kj . Now let p1, i be the probability that a person from city i travels exactly one leg to reach his destination, let p 2, i be the probability that he travels two legs, and let p 3 ...
... We define C as the n n matrix of three-leg travel probabilities, with the ij th element equal to l , k Ail Blk C kj . Now let p1, i be the probability that a person from city i travels exactly one leg to reach his destination, let p 2, i be the probability that he travels two legs, and let p 3 ...
Solutions to Exercises for Section 6
... c = d. So there are 10 reducible monic polynomials of degree 2, leaving 6 monic irreducible polynomials of degree 2. To find one of these irreducible polynomials, you could compute the 10 reducible ones and then take a polynomial not on the list, but that looks a little tedious, so you could just ch ...
... c = d. So there are 10 reducible monic polynomials of degree 2, leaving 6 monic irreducible polynomials of degree 2. To find one of these irreducible polynomials, you could compute the 10 reducible ones and then take a polynomial not on the list, but that looks a little tedious, so you could just ch ...
10 The Singular Value Decomposition
... equal to the transpose of V . Of course, this argument requires V to be full rank, so that the solution L to equation (69) is unique. However, V is certainly full rank, because it is made of orthonormal columns. Notice that V R = I cannot possibly have a solution when m > n, because the m × m identi ...
... equal to the transpose of V . Of course, this argument requires V to be full rank, so that the solution L to equation (69) is unique. However, V is certainly full rank, because it is made of orthonormal columns. Notice that V R = I cannot possibly have a solution when m > n, because the m × m identi ...
Notes
... that is, a rounding error in the (huge) u22 entry causes a complete loss of information about the a22 component. In this example, the l21 and u22 terms are both huge. Why does this matter? When L and U have huge entries and A does not, computing the product LU must inevitably involve huge cancellati ...
... that is, a rounding error in the (huge) u22 entry causes a complete loss of information about the a22 component. In this example, the l21 and u22 terms are both huge. Why does this matter? When L and U have huge entries and A does not, computing the product LU must inevitably involve huge cancellati ...
Linear Algebra and Matrices
... Take a set of vectors x1, x2,…,xn, all with the same number of elements: these vectors are linearly dependent if one can find a set of scalars c1, c2,…,cn non equal to zero such as: c1 x1+ c2 x2+…+ cn xn= 0 A set of vectors are linearly dependent if one of then can be expressed as a linear combinati ...
... Take a set of vectors x1, x2,…,xn, all with the same number of elements: these vectors are linearly dependent if one can find a set of scalars c1, c2,…,cn non equal to zero such as: c1 x1+ c2 x2+…+ cn xn= 0 A set of vectors are linearly dependent if one of then can be expressed as a linear combinati ...
On the second dominant eigenvalue affecting the power method for
... distribution vector associated with a Markov chain with memory [8]. Two questions arise and we intend to offer a clarification in this presentation. First, the assumption used to propose the Z-eigenvector computation is dubious and unjustifiable as our theory will show. Second, even if the proposed ...
... distribution vector associated with a Markov chain with memory [8]. Two questions arise and we intend to offer a clarification in this presentation. First, the assumption used to propose the Z-eigenvector computation is dubious and unjustifiable as our theory will show. Second, even if the proposed ...
Chapter 1 Linear and Matrix Algebra
... CHAPTER 1. LINEAR AND MATRIX ALGEBRA Moreover, when A is diagonalizable, the assertions of Lemma 1.5 remain valid, ...
... CHAPTER 1. LINEAR AND MATRIX ALGEBRA Moreover, when A is diagonalizable, the assertions of Lemma 1.5 remain valid, ...
