A question on matrices properties

In summary, there is a property of matrices called "Nilpotent Matrix" where for some matrices, if raised to a certain power (called the "index of nilpotence"), it will result in the zero matrix. This number can be found by repeatedly multiplying the matrix by itself until it reaches the zero matrix. There is no known easier method for determining this number.
  • #1
transgalactic
1,395
0
there is some property of matrices that i forgot
that says that for some kind of matrices there is a given number

that if we will put the given martices to the power of this given number
it will get the zero matrices

for example
0 a
a b

in the power of 3 will change for the first time to
0 0
0 0

what are the laws for this number 3

how do i know the number by looking at the given matrices
 
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  • #2
Such a matrix A is called "http://planetmath.org/encyclopedia/NilpotentMatrix.html [Broken]", and the smallest natural number n such that An=0 is usually called the "index of nilpotence". Try googling for information -- you'll find a lot.
 
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  • #3
i read about them
i understood the transformation
of each step

but i was told the the number comes from the size of the given matrices
which is not true in the case that i showed

the only way that i can find out the number is by practicly
step by step multiplying the matrix by itself.

is there an yeasier way??
 
  • #4
I'm not familiar with any easier general method.
 

1. What are matrices and what are their properties?

Matrices are rectangular arrays of numbers or symbols arranged in rows and columns. Their properties include being able to be added, subtracted, and multiplied, having a determinant, and being able to be transposed and inverted.

2. What is the determinant of a matrix and why is it important?

The determinant of a matrix is a scalar value that represents the size and orientation of the matrix. It is important because it is used to calculate the inverse of a matrix and to solve systems of linear equations.

3. How do you add or subtract matrices?

To add or subtract matrices, they must be of the same size. You simply add or subtract each corresponding element in the matrices to get the resulting matrix.

4. Can matrices be multiplied together?

Yes, matrices can be multiplied together, but the number of columns in the first matrix must match the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.

5. What does it mean to transpose a matrix?

Transposing a matrix means to switch its rows and columns. This is done by writing the first column of the original matrix as the first row of the transposed matrix, the second column as the second row, and so on. This can be useful in certain mathematical operations and can also help in representing data in a different way.

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