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GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well. In Python NumPy arrays implement the flatten method, [ note 1 ] while in R the desired effect can be achieved via the c() or as.vector() functions.
[4]: 7 Furthermore, as noted in the above formula, tr(A ⊤ B) = tr(B ⊤ A). These demonstrate the positive-definiteness and symmetry required of an inner product; it is common to call tr(A ⊤ B) the Frobenius inner product of A and B. This is a natural inner product on the vector space of all real matrices of fixed dimensions.
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.
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
A former director at a Massachusetts migrant shelter is speaking out against what he says were incidents of widespread violence, child sexual assault and rape at shelters in the state, including ...
Katch-McArdle equation Generally, TDEE calculators estimate BMR based on a person’s height, body weight, age, and gender assigned at birth. Then, they use a physical activity multiplier with the ...
Suppose : is a function taking as input a vector and outputting a scalar (). If all second-order partial derivatives of exist, then the Hessian matrix of is a square matrix, usually defined and arranged as = [].