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Is The Exponential Matrix Diagonalizable?

(Horn and Johnson 1994, p. 208). Matrix exponentials are important in the solution of systems of ordinary differential equations (e.g., Bellman 1970). Since most matrices are diagonalizable, it is easiest to diagonalize the matrix before exponentiating it.

How do you put a matrix into a power?

For a square matrix 𝐴 and positive integr 𝑘, the 𝑘th power of 𝐴 is defined by multiplying this matrix by itself repeatedly. That is, 𝐴 to the 𝑘th power is equal to 𝐴 multiplied by 𝐴 multiplied by 𝐴, and so on, multiplied by 𝐴, where there are 𝑘 instances of the matrix 𝐴.

How do you work out the exponential of a matrix?

If P is a projection matrix (i.e. is idempotent: P2 = P), its matrix exponential is: eP = I + (e 1)P.

What does the matrix exponential do?

Algorithm for Solving the System of Equations Using the Matrix Exponential We first find the eigenvalues of the matrix (linear operator) Calculate the eigenvectors and (in the case of multiple eigenvalues) generalized eigenvectors;

Does a matrix commute with its exponential?

We mention a drawback of matrix exponentials. In general . e A + B e A e B . The trouble is that matrices do not commute, that is, in general .

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