"The Matrix" revolutionized how we thought of the '90s and beyond, with a cast of cool cyberpunk heroes and villains. We rank ...
Abstract: Complex matrix derivatives play an important role in matrix optimization, since they form a theoretical basis for the Karush-Kuhn-Tucker (KKT) conditions associated with matrix variables. We ...
Stevens Institute, Hoboken, reports the universal identity P²+K²=1, uniting polarization with entanglement across setups and ...
Humans also create value through ethical restraint, the ability to recognize when not to cut corners, when to delay, and when to prioritize patient safety or scientific rigor over speed. That human ...
Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...
We study the solvability of the equation AX + XA * = XA + A * X = I. In particular, we obtain various criteria for the normality of A in terms of Hermitian solutions of the equation which satisfy ...
Abstract: An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high ...
In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has ...
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