Math 8502 — Homework I
... given by φt (x) = etA x, ψt (y) = etB y. Show that they are linearly conjugate if and only if the two matrices A, B are similar. b. Show that the linear flows determined by the matrices below are topologically conjugate but not linearly conjugate. Here a, b are any two positive numbers not both equa ...
... given by φt (x) = etA x, ψt (y) = etB y. Show that they are linearly conjugate if and only if the two matrices A, B are similar. b. Show that the linear flows determined by the matrices below are topologically conjugate but not linearly conjugate. Here a, b are any two positive numbers not both equa ...
PreCalculus - TeacherWeb
... *Elementary Row operations (see key concept on page 366): Each of the following row operations produces an equivalent augmented matrix. Interchange any 2 rows Multiply one row by a nonzero real number Add a multiple of one row to another row *See page 367 for comparison of Gaussian Elimination ...
... *Elementary Row operations (see key concept on page 366): Each of the following row operations produces an equivalent augmented matrix. Interchange any 2 rows Multiply one row by a nonzero real number Add a multiple of one row to another row *See page 367 for comparison of Gaussian Elimination ...
Eigenvalues - University of Hawaii Mathematics
... (3) In the case of a symmetric matrix, the n different eigenvectors will not necessarily all correspond to different eigenvalues, so they may not automatically be orthogonal to each other. However (if the entries in A are all real numbers, as is always the case in this course), it’s always possible ...
... (3) In the case of a symmetric matrix, the n different eigenvectors will not necessarily all correspond to different eigenvalues, so they may not automatically be orthogonal to each other. However (if the entries in A are all real numbers, as is always the case in this course), it’s always possible ...
Math 8306, Algebraic Topology Homework 11 Due in-class on Monday, November 24
... Due in-class on Monday, November 24 1. Complete the proof I messed up in class: Suppose X is a path-connected (based) space, M is a compact orientable manifold, and f : S 1 ∧X → M is a map inducing an isomorphism on homology with integer coefficients. Show that X has the same homology as a sphere S ...
... Due in-class on Monday, November 24 1. Complete the proof I messed up in class: Suppose X is a path-connected (based) space, M is a compact orientable manifold, and f : S 1 ∧X → M is a map inducing an isomorphism on homology with integer coefficients. Show that X has the same homology as a sphere S ...
D - Personal Web Pages
... Table creation: Creation of the frequency matrix FreqT SVD Construction: Compute the singular valued decompositions (A,S,B) of FreqT Vector Identification: For each document d, let vec(d) be the set of all terms in FreqT whose corresponding rows have not been eliminated in the singular matrix S Inde ...
... Table creation: Creation of the frequency matrix FreqT SVD Construction: Compute the singular valued decompositions (A,S,B) of FreqT Vector Identification: For each document d, let vec(d) be the set of all terms in FreqT whose corresponding rows have not been eliminated in the singular matrix S Inde ...
Definition: A matrix transformation T : R n → Rm is said to be onto if
... Definition: A matrix transformation T : Rn → Rm is said to be onto if evey vector in Rm is the image of at least one vector in Rn . Theorem 8.2.2: If T is a matrix transformation, T : Rn −→ Rn , then the following are equivalent (a) T is one-to-one (b) T is onto Example: Is the matrix transformation ...
... Definition: A matrix transformation T : Rn → Rm is said to be onto if evey vector in Rm is the image of at least one vector in Rn . Theorem 8.2.2: If T is a matrix transformation, T : Rn −→ Rn , then the following are equivalent (a) T is one-to-one (b) T is onto Example: Is the matrix transformation ...
Matrix Inverses Suppose A is an m×n matrix. We have learned that
... defined only if a particular compatibility condition € amongst the matrices being multiplied and is met their product: if AB makes sense, and A is m × n and B is p × q, then necessarily n must equal p and the product AB is m × q. For this and a number of other reasons (including for instance € that ...
... defined only if a particular compatibility condition € amongst the matrices being multiplied and is met their product: if AB makes sense, and A is m × n and B is p × q, then necessarily n must equal p and the product AB is m × q. For this and a number of other reasons (including for instance € that ...
Linear algebra - Practice problems for midterm 2 1. Let T : P 2 → P3
... Solution: This is not a subspace because it does not contain the zero polynomial. (c) W = {p(x) : the coefficient of x2 in p(x) is 0}. Solution: This is a subspace, because if p(x), q(x) have no x2 term, then neither do p(x) + q(x) and rq(x) for r ∈ R. 3. Let Mm×n be the vector space of m × n matric ...
... Solution: This is not a subspace because it does not contain the zero polynomial. (c) W = {p(x) : the coefficient of x2 in p(x) is 0}. Solution: This is a subspace, because if p(x), q(x) have no x2 term, then neither do p(x) + q(x) and rq(x) for r ∈ R. 3. Let Mm×n be the vector space of m × n matric ...
1= 1 A = I - American Statistical Association
... further "streamlining" is possible by working with the symmetric matrix A', which, in essence, merely exhibits the usual "normal" equations. This kind of procedure is easily explained without reference to the pseudoinverse, and is probably the simplest approach for small sized calculations. In large ...
... further "streamlining" is possible by working with the symmetric matrix A', which, in essence, merely exhibits the usual "normal" equations. This kind of procedure is easily explained without reference to the pseudoinverse, and is probably the simplest approach for small sized calculations. In large ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.