On Distributed Coordination of Mobile Agents
... The first two conditions of the theorem basically states that a finite set of stochastic matrices is LCP if and only if all finite products formed from the finite set of matrices are ergodic matrices themselves. This is a classical result due to Wolfowitz [19]. Note that ergodicity of each matrix is ...
... The first two conditions of the theorem basically states that a finite set of stochastic matrices is LCP if and only if all finite products formed from the finite set of matrices are ergodic matrices themselves. This is a classical result due to Wolfowitz [19]. Note that ergodicity of each matrix is ...
Chapter 9 The Transitive Closure, All Pairs Shortest Paths
... Then R, the transitive closure of A is (I+A)s for s >= n-1. How much work does this require? I + A requires n operations to insert 1's on the diagonal. s >= n let it be 2lg(n-1) + 1. i.e. s-1 is 2lg(n-1) Then (I+A)(s-1) is computed in lg(n-1) matrix multiplications. So R is computed in lg(n-1) + 1 m ...
... Then R, the transitive closure of A is (I+A)s for s >= n-1. How much work does this require? I + A requires n operations to insert 1's on the diagonal. s >= n let it be 2lg(n-1) + 1. i.e. s-1 is 2lg(n-1) Then (I+A)(s-1) is computed in lg(n-1) matrix multiplications. So R is computed in lg(n-1) + 1 m ...
NORMS AND THE LOCALIZATION OF ROOTS OF MATRICES1
... there exists a scalar K>0 such that the function defined by ||-4|| ~KV(A) for all A satisfies (iv). The ordinary Euclidean matrix norm possesses all four properties. Given any matrix norm, and an arbitrary vector as^O, ...
... there exists a scalar K>0 such that the function defined by ||-4|| ~KV(A) for all A satisfies (iv). The ordinary Euclidean matrix norm possesses all four properties. Given any matrix norm, and an arbitrary vector as^O, ...
The Elimination Method for solving large systems of linear
... In this section we will learn a general method for finding possible solutions to a linear system of equations. The method involves systematic elimination of the unknown from each equation in turn. We will explain the method with examples. Example 1. Solve the system ...
... In this section we will learn a general method for finding possible solutions to a linear system of equations. The method involves systematic elimination of the unknown from each equation in turn. We will explain the method with examples. Example 1. Solve the system ...
Arithmetic operations
... Kronecker tensor product. KRON(X,Y) is the Kronecker tensor product of X and Y. The result is a large matrix formed by taking all possible products between the elements of X and those of Y. ...
... Kronecker tensor product. KRON(X,Y) is the Kronecker tensor product of X and Y. The result is a large matrix formed by taking all possible products between the elements of X and those of Y. ...
Steiner Equiangular Tight Frames Redux
... rows and unit-norm equiangular columns. ETFs seem to be very rare. Comparing the number of entries in an ETF’s synthesis operator Φ against the number of conditions they must satisfy, it is surprising that several nontrivial infinite families of ETFs have been discovered. Each of these known constru ...
... rows and unit-norm equiangular columns. ETFs seem to be very rare. Comparing the number of entries in an ETF’s synthesis operator Φ against the number of conditions they must satisfy, it is surprising that several nontrivial infinite families of ETFs have been discovered. Each of these known constru ...
Introduction to Matrix Algebra
... where A is a square matrix of eigenvectors and D is a diagonal matrix with the eigenvalues on the diagonal. If there are n variables, both A and D will be n by n matrices. Eigenvalues are also called characteristic roots or latent roots. Eigenvectors are sometimes refereed to as characteristic vecto ...
... where A is a square matrix of eigenvectors and D is a diagonal matrix with the eigenvalues on the diagonal. If there are n variables, both A and D will be n by n matrices. Eigenvalues are also called characteristic roots or latent roots. Eigenvectors are sometimes refereed to as characteristic vecto ...
