MATLAB Mathematics - SERC - Index of

Matrix Powers and Exponentials
Y =
145.0000 -207.0000 81.0000
-207.0000 298.0000 -117.0000
81.0000 -117.0000 46.0000
Fractional powers, like A^(2/3), are also permitted; the results depend upon
the distribution of the eigenvalues of the matrix.
Element-by-Element Powers
The .^ operator produces element-by-element powers. For example,
X = A.^2
A =
1 1 1
1 4 9
1 9 36
Exponentials
The function
sqrtm(A)
computes A^(1/2) by a more accurate algorithm. The m in sqrtm distinguishes
this function from sqrt(A) which, like A.^(1/2), does its job
element-by-element.
A system of linear, constant coefficient, ordinary differential equations can be
written
dx ⁄ dt = Ax
where x = x(t) is a vector of functions of t and A is a matrix independent of t.
The solution can be expressed in terms of the matrix exponential,
xt () = e tA x( 0)
The function
expm(A)
1-35