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Matrix Power

Tool to calculate matrix powers in algebra. Matrix power consists in exponentiation of the matrix (multiplication by itself).

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Matrix Power -

Tag(s) : MATRIX

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Matrix Power

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Matrix Power



Tool to calculate matrix powers in algebra. Matrix power consists in exponentiation of the matrix (multiplication by itself).

Answers to Questions

How to calculate the matrix power n?

Consider \( M \) a square matrix of \( m \) lines and \( m \) columns. The calculation of the nth power of the matrix M is denoted by \( M^n \) and consists of multiplying the matrix n times by itself.

$$ \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} ^2 = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \times \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} = \begin{pmatrix} 7 & 10 \\ 15 & 22 \end{pmatrix} $$

The size of the resulting matrix is identical to the original matrix M; i.e. \( m \) lines and \( m \) columns.

Calculating matrix power only works for square matrices.

How to compute a negative power of a matrix?

Calculating \ (M^{-n} \) is equivalent to \( M^{-1 \times n} \). Thus, you can calculate the inverse of the matrixhref and then perform with it an exponentiation to the power n.

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