Mat Calc

Here are sample expressions showing the functions and operators that the calculator supports.

Addition: A + B adds matrices A and B together. Likewise, A - B subtracts A and B. A and B must have the same size.

Assignment: C = A + B adds A and B together and assigns the result to C. If C does not exist, then it is created and added to the list of variables. If C already exists, then C is overwritten with the new value.

Multiplication: C = A * B computes the matrix product of nxm matrix A and mxp matrix B producing nxp matrix C as the result. Matrix multiplication is only defined if the number of columns in A is the same as the number of rows in B (i.e., m). 2 * A performs scalar multiplication by multiplying every element of matrix A by the scalar 2 with the resulting matrix having the same size as A.

Transpose: B = 'A transposes nxm matrix A, returning an mxn matrix B in which the rows of B are the columns of A and the columns of B are the rows of A.

Gaussian Elimination: ref(A) performs Gaussian elimination, yielding the row-echelon form of A. rref(A) performs Gauss-Jordan elimination, yielding the reduced row-echelon form of A.

Inverse: inv(A) calculates the inverse of A. A must be square to compute its inverse.

Solve: X = solve(A, B) solves the system of linear equations Ax=b for each column vector b in matrix B, storing each solution x as a column vector in matrix X. A and B must have the same number of rows. B / A also performs this function.

Determinant: det(A) calculates the determinant of A. A must be square to compute its determinant.

Rank: rank(A) calculates the rank of matrix A, the number of linearly independent rows or columns. null(A) calculates the dimension of the null space of A, or nullity of A.

Trace: tr(A) computes the trace of A, the sum of the elements along the main diagonal of A.

Augment: aug(A, B) creates an augmented matrix from A and B. The augmented matrix consists of the columns of A followed by the columns of B.

Sub-matrix: sub(A, 0, 1, 2, 3) creates a sub-matrix from A. The sub-matrix is the 2x3 matrix starting with the element at row 0 and column 1 in A.

Equality: A == B compares matrices A and B for equality. If A and B have the same sizes and the same elements, then the result is 1; otherwise, the result is 0. A != B compares for inequality where the result is 1 if either A and B have different sizes or at least 1 element differs between the two matrices; otherwise the result is 0.

Comparison: A < B compares matrices A and B, returning 1 if every element in A is strictly less than every element in B; otherwise, 0 is returned. The comparison operators are <, <=, >, and >=. A and B must have the same size.

Exponentiation: A^3 multiples A with itself 3 times. The exponent (e.g., 3) must be a non-negative integer. If the exponent is 0, then the resulting matrix has the same size as A and 1 for every element. The base (e.g., A) can be either a matrix or a scalar.