Verified answer

Konstantin, it's a matrix...

Find the eigenvalues by solving

x^2 + 3x - 4 = 0.

You get

x = 1, -4.

This means we can set

D =

1 0

0 -4

Then find some eigenvectors. For x=1,

-1

20

is an eigenvector. For x=-4,

-1

10

is an eigenvector.

Therefore we may set

S =

-1 -1

20 10.

Your notation for A is a bit ambiguous; I assume A = -(9/100) - (0.5/6)? Like so: http://dl.dropbox.com/u/17850283/yanswers_jim.png

In that case, the equation S⁻¹ A S = D would be as follows:

S⁰ A = D

since S⁻¹ * S = S⁻¹ * S¹; multiplication means you add the two exponents together, which gives you an exponent of 0. ANY number to the power of 0 is 1.

If you don't understand this, think of S⁻¹ as 1 over S. When you multiply 1 / S by S, the two S's cancel out, leaving you with 1.

Therefore, your equation ends up being:

1 A = D → D = -(9/100) - (0.5/6) = -13/75

As for S, since S⁻¹ * S will cancel out it the original equation, you'll be left with -13/75 = -13/75; therefore, S can be ANY real number.

D = A = -13/75

S = any real number

Again, your notation for A is confusing, so this may not be the solution. Let me know if I interpreted it wrong.