There are different properties of determinants that enables us to calculate determinants easily. For example, one of the property is that if all the elements of any row or column of matrix are equal to zero then determinant of such a matrix is equal to zero. Another
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How to find Eigen values and Eigen Vectors of a matrix?
For example, we are given any n x n matrix A and we want to calculate its Eigen values and eigen vectors. Then, we must have non-zero vector x such that Ax=λx, where λ is an Eigen value and x is eigen vector. When we solve this equation, we get values of λ and x.
What are tridiagonal matrices?
Tridiagonal matrices are the matrices which are having non-zero elements on the diagonal, super diagonal and subdiagonal. All the rest of the elements are zeros.
Example of an Idempotent Matrix
Example of Nilpotent Matrix
Note that matrix A is said to be Nilpotent if
where m is any integer and
is a null matrix of same order as of A.
Lets take example of matrix A which is nilpotent.
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