A matrix equation is an equation where the variable is a matrix itself. We can use addition, subtraction, and scalar multiplication to solve matrix equations.
The first task is to break down the model equation into a set of first-order equations as follows. dudx=z,u0=1.dzdx=x+3u1.2,z0=0. Euler method. The Euler formulas are given below, and Table I summarizes the computational results from two steps. zi+1=zi+Δxxi+3ui1.2.ui+1=ui+...
We show that the discrete operator stemming from time-space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure ...
Then Lj+1(u) is found from vj+1. The elements of Lj+1(u) can be either dependent or independent. If elements in Lj+1(u) are independent, then the Bellman equation (14.55) can be solved iteratively using stored data to find L⋆(u) and the optimal control policy is u⋆. The ...
Namely, let LwFQ be the elimination of the variable w from the functions FQ,1, FQ,2. This is given by the resultant Rw(FQ,1, FQ,2) of the functions with respect to the variable w. We have LwFQ = Rw(FQ,1, FQ,2) = det q1 = f. Now suppose that p1(x, y, z) = y, ...
When there is a missing variable term in an equation, the coefficient is 0.How To: Given a system of equations, write an augmented matrix. Write the coefficients of the x-terms as the numbers down the first column. Write the coefficients of the y-terms as the numbers down th...
diagonal matrix created from the row or column vector the number of zeros on the diagonal of [floor( ),floor( )], the , element of the matrix named ; missing if or are out of range or if matrix does not exist a copy of Stata internal system matrix systemname a matrix whose , elemen...
2.1.1453 Part 1 Section 21.2.2.43, dispEq (Display Equation) 2.1.1454 Part 1 Section 21.2.2.44, dispRSqr (Display R Squared Value) 2.1.1455 Part 1 Section 21.2.2.47, dLbl (Data Label) 2.1.1456 Part 1 Section 21.2.2.48, dLblPos (Data Label Position) 2.1.1457 Part 1 Sec...
and of a 3×3 matrix by (C.21)|a11a12a13a21a22a23a31a32a33|=a11a22a33+a21a32a13+a31a12a23−a11a32a23−a21a12a33−a31a22a13 The determinant of the product of two matrices is equal to the product of the determinants, that is, (C.22)|ab|=|a||b| From this equation and Eq...
From Eq. (1.9), and using the definition of Eq. (1.14), the following equation is obtained. MⅆW2ⅆt+c·W2+K·W1=−M·y¨ This equation can be written as the following set matrix equations (1.15){ⅆW1ⅆtⅆW2ⅆt}=[01−KM−cM]{W1W2}+{0−1}{y¨(t)} and (...