Anti-Hadamard matrices, coin weighing, threshold gates and
... For a real matrix A, the spectral norm of A is defined by kAks = supx6=0 |Ax|/|x|. If A is invertible, the condition number of A is c(A) = kAks kA−1 ks . This quantity measures the sensibility of the equation Ax = b when the right hand side is changed. If c(A) is large, then A is called ill-conditio ...
... For a real matrix A, the spectral norm of A is defined by kAks = supx6=0 |Ax|/|x|. If A is invertible, the condition number of A is c(A) = kAks kA−1 ks . This quantity measures the sensibility of the equation Ax = b when the right hand side is changed. If c(A) is large, then A is called ill-conditio ...
Chapter 2 - Systems Control Group
... representation of x in this new basis (See the Appendix to Chapter 2 for more details on change of basis). We call the transformation V featured in the change of basis a similarity transformation. Theorem 2.3: (A, B) is controllable if and only if (V −1 AV, V −1 B) is controllable for every nonsingu ...
... representation of x in this new basis (See the Appendix to Chapter 2 for more details on change of basis). We call the transformation V featured in the change of basis a similarity transformation. Theorem 2.3: (A, B) is controllable if and only if (V −1 AV, V −1 B) is controllable for every nonsingu ...
On Leonid Gurvits`s Proof for Permanents
... bounds for the permanent (see the book of Minc [12]). In this paper we will consider only lower bounds. Indeed, most interest in the permanent function came from the famous van der Waerden conjecture [16] (in fact formulated as a question), stating that the permanent of any n × n doubly stochastic m ...
... bounds for the permanent (see the book of Minc [12]). In this paper we will consider only lower bounds. Indeed, most interest in the permanent function came from the famous van der Waerden conjecture [16] (in fact formulated as a question), stating that the permanent of any n × n doubly stochastic m ...
LU Factorization
... Linear Algebra Review • Now that we have covered some examples of solving linear systems, there are several important questions: – How many numerical operations does Gaussian Elimination take? That is, how fast is it? – Why do we use LU factorization? In what cases does it speed up calculation? – H ...
... Linear Algebra Review • Now that we have covered some examples of solving linear systems, there are several important questions: – How many numerical operations does Gaussian Elimination take? That is, how fast is it? – Why do we use LU factorization? In what cases does it speed up calculation? – H ...
Transmission through multiple layers using matrices - Rose
... We will consider transmission through a series of layers. We will tackle light going through different regions at normal incidence, and the context is a multi-layer optical filter. But the same layout applies to a series of layers of acoustical material, or to a series of layers of semiconductors wh ...
... We will consider transmission through a series of layers. We will tackle light going through different regions at normal incidence, and the context is a multi-layer optical filter. But the same layout applies to a series of layers of acoustical material, or to a series of layers of semiconductors wh ...
Multiequilibria analysis for a class of collective decision
... ONLINEAR interconnected systems are used in broadly different contexts to describe the collective dynamical behavior of an ensemble of “agents” interacting with each other in a non-centralized manner. They are used for instance to represent collective decision-making by animal groups [1], [2], [3], ...
... ONLINEAR interconnected systems are used in broadly different contexts to describe the collective dynamical behavior of an ensemble of “agents” interacting with each other in a non-centralized manner. They are used for instance to represent collective decision-making by animal groups [1], [2], [3], ...
Multiuser Decision-Feedback Receivers for the General Gaussian
... readily seen that the nonzero elements of opt are the same as the rst i , 1 elements of Rf for any f that is used. That is, opt simply removes the interference from the previous users. Since, for any user i, B has removed the interference of users 1 to i , 1, user i \looks" like a rst user. Ther ...
... readily seen that the nonzero elements of opt are the same as the rst i , 1 elements of Rf for any f that is used. That is, opt simply removes the interference from the previous users. Since, for any user i, B has removed the interference of users 1 to i , 1, user i \looks" like a rst user. Ther ...
Mitri Kitti Axioms for Centrality Scoring with Principal Eigenvectors
... Example 1 demonstrates that we can associate an adjacency matrix to a graph. On the other hand, for a given positive matrix we can find a corresponding graph in which there is an edge between nodes i and j if aij > 0. Without loss of generality we may assume that the weight of the edge is aij . Let ...
... Example 1 demonstrates that we can associate an adjacency matrix to a graph. On the other hand, for a given positive matrix we can find a corresponding graph in which there is an edge between nodes i and j if aij > 0. Without loss of generality we may assume that the weight of the edge is aij . Let ...
Course Title - obrienprecal
... anyway. There will be no food or drink allowed in the room, except water. Academic honesty: Always submit your own work, but feel free to discuss homework and class work with classmates. Copying someone elses work or cheating is not allowed and will result in a zero on the assignment and disciplinar ...
... anyway. There will be no food or drink allowed in the room, except water. Academic honesty: Always submit your own work, but feel free to discuss homework and class work with classmates. Copying someone elses work or cheating is not allowed and will result in a zero on the assignment and disciplinar ...
Matrix functions preserving sets of generalized nonnegative matrices
... 2. Matrix functions preserving PFn. In this section, we completely characterize matrix functions preserving the set of real n × n eventually positive matrices, PFn. For n = 1, these functions are simply functions f which are holomorphic on an open set Ω ⊆ C containing the positive real axis and whic ...
... 2. Matrix functions preserving PFn. In this section, we completely characterize matrix functions preserving the set of real n × n eventually positive matrices, PFn. For n = 1, these functions are simply functions f which are holomorphic on an open set Ω ⊆ C containing the positive real axis and whic ...
MATH 105: Finite Mathematics 2
... Matrix Multiplication If we know how to multiply a row vector by a column vector, we can use that to define matrix multiplication in general. Matrix Multiplication If A is an m × n matrix and B is an n × k matrix, then the produce AB is defined to be the m × k matrix whose entry in the ith row, jth ...
... Matrix Multiplication If we know how to multiply a row vector by a column vector, we can use that to define matrix multiplication in general. Matrix Multiplication If A is an m × n matrix and B is an n × k matrix, then the produce AB is defined to be the m × k matrix whose entry in the ith row, jth ...
M.4. Finitely generated Modules over a PID, part I
... of the first type gives a matrix with r in the (i, 1) position. Then interchanging the first and i–th rows yields a matrix with r in the (1, 1) position. Since d(r) < d(α), we are done. Proof of Proposition M.4.7. If A is the zero matrix, there is nothing to do. Otherwise, we proceed as follows: Ste ...
... of the first type gives a matrix with r in the (i, 1) position. Then interchanging the first and i–th rows yields a matrix with r in the (1, 1) position. Since d(r) < d(α), we are done. Proof of Proposition M.4.7. If A is the zero matrix, there is nothing to do. Otherwise, we proceed as follows: Ste ...
EGR2013 Tutorial 8 Linear Algebra Outline Powers of a Matrix and
... A scalar is a quantity that is determined by its magnitude; A vector is a quantity that is determined by both its magnitude and its direction. Equality of Vectors: two vectors a and b are equal, if they have the same length and the same direction. Representations: in Cartesian coordinate system, the ...
... A scalar is a quantity that is determined by its magnitude; A vector is a quantity that is determined by both its magnitude and its direction. Equality of Vectors: two vectors a and b are equal, if they have the same length and the same direction. Representations: in Cartesian coordinate system, the ...
