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Contents >> Applied Mathematics >> Matrix Algebra >> Principles of Matrix Calculation >> Powers of matrices

Matrix Algebra - Powers of matrices

Powers of matrices

Let A – a square matrix and  n – a natural number. Then the n-th power of the matrix A is:

Besides it is considered, that , where Е – an identity matrix.
If  A is a regular (non-singular) matrix, it is possible to enter a negative power of a matrix:

For powers of matrices with the whole indices the following rules take place:

If A and B – square matrices of the same orders, and АВ = ВА, then Newton’s binomial formula takes place:


E x a m p l e  [1] .  Find

S o l u t i o n .

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Last updated: April 30, 2015.