Thread: Theoretical Question

We have a real 2x2 matrix A with 2 distinct real eigenvalues, lambda1 and lambda 2. explain the formula detA = lambda1(lambda 2) geometrically, thinking of module(detA) as an explansion facor. illustrate your explanation with a sketch. can you explain this similarly for 3x3 matrices?

i dont even know where to begin! and thanks for the help in advance!

Originally Posted by satweety12

We have a real 2x2 matrix A with 2 distinct real eigenvalues, lambda1 and lambda 2. explain the formula detA = lambda1(lambda 2) geometrically, thinking of module(detA) as an explansion facor. illustrate your explanation with a sketch. can you explain this similarly for 3x3 matrices?

i dont even know where to begin! and thanks for the help in advance!

I'm not completely sure whether the question is clear enough to me, but I can think of the following: if the matrix has two eigenvalues , then is similar to the matrix , and since we know that , and this last one has a very nice and simple geometric interpretation we get (?) what we want: it is the "volume" (generalized algebraic volume, which in this case is 2-dimensional volume = usual area) of the parallelogram (rectangle in this case) generated by the 2-dimensional vectors

Tonio

thanks!