Matrix Calculus

Matrix Calculus is the best current application calculator for mathematical operations involving numbers, matrices and multi-dimensional matrices for real and complex numbers.

it’s able to perform all standard mathematical calculations on numbers, vectors (matrices of size 1) and matrices from 2 to 5 dimensions.

Numbers can be real or complex, both in normal operations and in matrices;

Matrix Calculus also has a key that allows you to operate exclusively in the real field or in the complex field,

thus giving an error if the field is real and the result of the operation is complex;

to operate on complex numbers Matrix Calculus requires the payment of an in-app.

The only limits for matrices are the following:

- Dimensions of a matrix from 1 to 5

- Maximum total length of a matrix less than 3200

- Maximum length of a matrix dimension = 50

The possible operations are the standard of mathematics and the following matrix operations:

* = product matrix

/ = division of two matrices, or product of the inverse matrix

^ = power of a matrix

+ = sum matrix

- = difference matrix

Det = Determinant

Tra = matrix transpose

Inv = matrix inverse

Adj = adjoint matrix

tr(A) = trace of matrix A

Unit = matrix unit

Rank = matrix rank

Erf = error function erf

REF = matrix in Row Echelon Form (system solution)

The following matrix operations are operative only with the Pro version:

Inv+ = Moore - Penrose pseudo inverse

Eigen = matrix eigenvalues

Evect = matrix eigenvectors

Vsing = matrix singular values S

Uvect = left vector singular matrix U

Vvect = right vector singular matrix V

Dsum = matrix direct sum

Outer = outer product

L(L*L’) = Lower triangolar matrix L so that A = L*L’

Q(Q*R) = Left matrix Q so that A = Q*R

R(Q*R) = Wright matrix R so thar A = Q*R

Jordan = Jordan matrix J

||A|| = Frobenius norm

e^A = exponential of matrix A

√ A = square root matrix

If the matrix allows, it is also possible to calculate a matrix function, where the function is one of those of the calculator, for example (A = matrix):

lne (A), log (A), sin (A) cos (A), tan (A), sinh (A), arcsin (A), arctanh (A)