The dimensions of a matrix, A, are usually denoted as m × n. … this refers that A has m rows and n columns. Once bearing on a particular worth encompassing matrix, called a part, a variable with 2 subscripts is commonly wont to denote every element this implies its position in the matrix.

Power of a matrix

For the intents of this calculator, "power of a matrix" refers that to raise a given matrix to a given power. this implies, once utilizing the Matrix Calculator, "Power of 2two for a given matrix, A, means A2. Exponents for matrices operate within the same means as they commonly waste mathematics, except that matrix operation rules additionally apply, therefore only sq. matrices (matrices with an equal range of rows and columns) may be raised to an influence. this is often as a result of a non-square matrix, A, cannot be increased by itself. A × A during this case isn't possible to work out. ask the matrix operation section, if necessary, for a refresher on how to multiply matrices. Given:

A = 1 3
2 1

A raised to the power of two is:

A2 = 1 3
2 1

2

= 1 3
2 1

× 1 3
2 1

= 7 6
4 7

As with exponents in different mathematical contexts, A3, would equal A × A × A, A4 would equal A × A × A × A, and so on.

Transpose of a matrix

Transpose of a matrix

The transpose of a matrix, generally, indicated with a "T" as an exponent, also is an continue that flips a matrix over its diagonal. Then, This leads to switching the row and column indices of a matrix, meaning that aij in matrix A, becomes aji in AT. If necessary, refer on top of for description of the notation used.

An m × n matrix, transposed, would thus become an n × m matrix, as shown within the examples below:

A = 1 3
2 1

AT = 1 2
3 1

B = 20 23 4 4
44 51 8 8

BT = 20 44
23 51
4 8
4 8

Determinant of a matrix

Firstly, The determinant of a matrix is a worth that may be computed from the elements of a matrix. Moreover, it's employed in linear algebra, calculus, and different mathematical contexts. for instance, the determinant may be wont to compute the inverse of a matrix or to resolve a system of linear equations.

Also, There are variety of strategies and formulas for calculating the determinant of a matrix. So, The Leibniz formula and the Laplace formula ar 2 ordinarily used formulas.

Determinant of a 2 × 2 matrices:

The determinant of a 2 × 2 matrix may be calculated using the philosopher formula, then, that involves some basic arithmetic. Given matrix A:

A = a b
c d

The determinant of A using the philosopher formula is:

|A| = a b
c d