 # Matrix Properties Calculator

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### How does the Matrix Properties Calculator work?

Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A-1
* Transpose = AT
* Eigen equation (characteristic polynomial) = det|λI - A|
* Trace = tr(A)
* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form
* Dimensions of |A| m x n
* Order of a matrix
* Euclidean Norm ||A||
* Magic Sum if it exists
* Determines if |A| is an Exchange Matrix
This calculator has 1 input.

### What 2 formulas are used for the Matrix Properties Calculator?

1. Order of a matrix = m x n
2. Magic Sum = n(n2 + 1)/2

For more math formulas, check out our Formula Dossier

### What 11 concepts are covered in the Matrix Properties Calculator?

the transpose of a cofactor matrix
determinant
value computed from a square matrix
det(A) or |A|
dimension
the number of rows by the number of columns for a matrix
echelon
eigen
inverse
opposite or contrary in position
matrix
a rectangular array of numbers or symbols which are generally arranged in rows and columns
matrix properties
norm
a vector space whose elements (vectors) are matrices (of given dimensions).
polynomial
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
transpose
an operator which flips a matrix over its diagonal. It switches the rows and columns indices of the matrix