I compute the following matrix: D = b'Ab, where A is a symmetric covariance matrix. D is high-dimensional and must be symmetric by definition. But when I apply a functiion "issymmetric" to D, Matlab returns 0 meaning that it is not symmetric. I guess the problem is the way Matlab h...
symmetric matrix n (Mathematics)mathsa square matrix that is equal to its transpose, being symmetrical about its main diagonal. Askew symmetric matrixis equal to the negation of its transpose. Compareorthogonal matrix Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © Harper...
A square matrix may also be symmetric if it can be reflected along the main diagonal (from upper left down to lower right) while remaining the same. This is summarized in the following definition. Definition 6.6: Symmetric Matrix A square matrix is called symmetric if A=AT. Next follows...
Matrix-matrix operations . . . . . . . . . 110 2.4.1 cublasSgemm - matrix-matrix multiplication . . . . . 110 2.4.2 cublasSgemm - unified memory version . . . . . . . . 113 2.4.3 cublasSsymm - symmetric matrix-matrix multiplication115 2.4.4 cublasSsymm - unified memory ...
matrix myV=e(V) after running thebscommand, the matrix that is saved is not the variance–covariance matrix for my model (i.e., the diagonal of this matrix does not contain the square of the standard errors of the coefficients that are reported in the output). How can I retrieve the ...
The Arnoldi process also produces an(n+1)-by-nupper Hessenberg matrixH~nwith AQn=Qn+1H~n. For symmetric matrices, a symmetric tri-diagonal matrix is actually achieved, resulting in theminresmethod. Q n ∥rn∥=∥b−Axn∥=∥b−A(x0+Qnyn)∥=∥r0−AQnyn∥=∥βq1−AQnyn∥=∥β...
You are asked to transform the matrix into a special form using these operations. In that special form all the ones must be in the cells that lie below the main diagonal. Cell of the matrix, which is located on the intersection of the i-th row and of the j-th column, lies below th...
Therefore, the Hessian is always a symmetric matrix. It plays a prominent role in the sufficiency conditions for optimality as discussed later in this chapter. It will be written as (4.8)H=[∂2f∂xj∂xi];i=1ton,j=1ton The gradient and Hessian of a function are calculated in Example...
Here, theτxandτzare Pauli matrices,τ0is a 2 × 2 unit matrix. This system has both TRS and IS, thus, the component ofτymust be zero11. We can obtain the eigenvalues of the two-level system by diagonalizing the 2 × 2 effective Hamiltonian and the results are[Math Proce...
The necessary and sufficient conditions for the existence of and the expressions for the symmetric solutions of matrix equations (I) AX + YA = C , (II) AXA T + BYB T = C , and (III) ( A T XA , B T XB ) = ( C, D ) are derived. In addition, the minimum-2-norm least-...