The way to solve a matrix equation is to follow the same procedure for solving linear equations. You can use the subtraction and addition properties of equality to solve the matrix. Example #1: Solve X - [5 2 1] = [-1 2 4]Notice that X represents a matrix. A matrix equation is ...
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc. Want to thank TFD for its existence?Tell a friend about us, add a link to this page, or visitthe webmaster's page for free fun content. ...
Moreover, if the matrix D(k)DT(k) is regular, then the “⩽” symbol in this equation can be replaced by the “=” symbol if and only if λ belongs to the set {0,1} or Kx1(k)−Kx2(k) is not of FRR. Proof To shorten mathematical expressions and present essential ideas be...
For example, to solve the matrix equation AX = B, when A is a square matrix and X and B are column vectors, left division should be used: X = A\B. Whereas to solve XC = B, with X and B row vectors and C as a transposed matrix of A, right division should be used: X = B...
3. Solve linear equation of any number of variables using 1.Inverse Matrix method 2.Cramer's Rule method 3.Gauss-Jordan Elimination method 4.Gauss Elimination Back Substitution method 5.Gauss Seidel method 6.Gauss Jacobi method 7.Elimination method ...
for all \(({\textbf{A}}', {\textbf{x}}')\) in N by the first equation (A7). In order to compute the last derivative above, we appeal to the formula for the derivative of the pseudoinverse operation. Specifically, if B is a matrix, then we have that $$\begin{aligned} \frac{...
An alternative to deriving a high-order differential system equation is to represent the system as a set of simultaneous first-order differential equations of the system’s state variables, which are its energy storage variables. This is known as state-s
Those tion for computing Fredholm integral equation of the second kind. The main t... C Gu,J Shen - 《高等学校计算数学学报(英文版)》 被引量: 6发表: 2007年 Computational Aspect For Function-Valued Padé-Type Approximation The computational problems of two special determinants are investigated....
A matrix A∈Rn×n is asymptotically stable if and only if there exists a positive definite solution to the Lyapunov equation (2.13), where C=Ct<0. 2.3.8 Simulation example 2.1 Consider A=[123321],B=[2123]. Simple computation shows that (A⊗B)=[B2B3B3B2BB]=[214263234669634221694623]....
In the above equation, I is the identity matrix. We have added the equation to update the particle density, which is for example needed to calculate the equations of state. For a hypoelastic constitutive model, one needs to compute the strain increment Δep=symLpt+ΔtΔt and using it ...