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The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a linear transformation on matrices. In particular, vec ( A B C ) = ( C T ⊗ A ) vec ( B ) {\displaystyle \operatorname {vec} (ABC)=(C^{\mathrm {T} }\otimes A)\operatorname {vec} (B)} for matrices A , B , and C of dimensions k ...
In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is A X A H − X + Q = 0 {\displaystyle AXA^{H}-X+Q=0} where Q {\displaystyle Q} is a Hermitian matrix and A H {\displaystyle A^{H}} is the conjugate transpose of A {\displaystyle A} , while the continuous-time Lyapunov equation is
In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis.
A simple arithmetic calculator was first included with Windows 1.0. [6]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Mac OS calculator: Proprietary: macOS: Double (64 bit) Yes Yes Yes GNOME Calculator: GPL-3.0-or-later: Linux, BSDs, macOS: Arbitrary decimal Yes Yes Yes KCalc: GPL-2.0-or-later: Linux, BSDs, macOS: Arbitrary decimal Yes Yes Yes Windows Calculator: MIT: Windows: ≥32 decimal Yes Yes Yes WRPN Calculator: Public domain: Windows, Linux, macOS ...
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(The Center Square) – The Georgia Court of Appeals removed Fulton County District Attorney Fani Willis from prosecuting the election interference case against Donald J. Trump and others. The ...
A vector processor, by contrast, even if it is single-issue and uses no SIMD ALUs, only having 1-wide 64-bit LOAD, 1-wide 64-bit STORE (and, as in the Cray-1, the ability to run MULTIPLY simultaneously with ADD), may complete the four operations faster than a SIMD processor with 1-wide LOAD, 1-wide STORE, and 2-wide SIMD.