Matrix Calculus is the best current application for mathematical operations involving numbers, matrices and multi-dimensional matrices;
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)
