You're missing an equation that results from ##M^2 = 0##.Aleoa said:
Mark44 said:
Yes, you already said that in post #1, but you're not using the fact that the matrix is nilpotent.Aleoa said:
Using the fact that tr(M) = 0, you have a + d = 0.Aleoa said:
Mark44 said:
Aleoa said:
PeroK said:
Aleoa said:
A 2x2 nilpotent matrix is a square matrix with 2 rows and 2 columns that has the property that when raised to a certain power, the resulting matrix becomes a zero matrix.
To construct a 2x2 nilpotent matrix, you can start with a matrix with zeros in all entries except for the top right corner. Then, you can choose any non-zero number to fill in the bottom left entry. This will result in a matrix that, when squared, becomes a zero matrix.
Nilpotent matrices are important in linear algebra and other areas of mathematics because they have unique properties that make them useful for solving equations and studying systems of equations.
No, a 2x2 nilpotent matrix can only have non-zero entries in the top right and bottom left positions. This is because any other non-zero entry would result in the matrix not being nilpotent.
A nilpotent matrix is different from a diagonal matrix in that a diagonal matrix can have non-zero entries in any position along the main diagonal, while a nilpotent matrix can only have non-zero entries in the top right and bottom left positions. Additionally, a diagonal matrix has distinct eigenvalues, while a nilpotent matrix has at least one eigenvalue of 0.
