Create symbolic matrix variable - MATLAB symmatrix - MathWorks Deutschland (2024)

Create two symbolic matrix variables with size 2-by-3. Nonscalar symbolic matrix variables are displayed as bold characters in the Live Editor and Command Window.

A = symmatrix('A',[2 3])

A =$$A$$

B = symmatrix('B',[2 3])

B =$$B$$

Add the two matrices. The summation of the two symbolic matrix variables is denoted by the matrix notation $$\text{A}+\text{B}$$.

X = A + B

X =$$A+B$$

Symbolic matrix variables represent matrices, vectors, and scalars in compact matrix notation. When representing nonscalars, these variables are noncommutative. When mathematical formulas involve matrices and vectors, writing them using symbolic matrix variables is more concise and clear than writing them componentwise.

Create two symbolic matrix variables.

A = symmatrix('A',[2 2]);B = symmatrix('B',[2 2]);

Check the commutation relation for multiplication between two symbolic matrix variables.

A*B - B*A

ans =$$A\hspace{0.17em}B-B\hspace{0.17em}A$$

isequal(A*B,B*A)

ans = logical 0

Check the commutation relation for addition between two symbolic matrix variables.

isequal(A+B,B+A)

ans = logical 1

Create 3-by-3 and 3-by-1 symbolic matrix variables.

A = symmatrix('A',3)

A =$$A$$

X = symmatrix('X',[3 1])

X =$$X$$

Find the Hessian matrix of $${\text{X}}^T\text{A}\text{X}$$. Derived equations involving symbolic matrix variables are displayed in typeset as they would be in textbooks.

f = X.'*A*X;H = diff(f,X,X.')

H =$$A^{\mathrm{T}}+A$$

Create a Hilbert matrix of order 4. The data type of the matrix is double.

H = hilb(4)

H = 4×4 1.0000 0.5000 0.3333 0.2500 0.5000 0.3333 0.2500 0.2000 0.3333 0.2500 0.2000 0.1667 0.2500 0.2000 0.1667 0.1429

class(H)

ans = 'double'

Convert the numeric matrix to a symbolic matrix variable. The data type of the converted matrix is symmatrix.

X = symmatrix(H)

X =
$$\begin{array}{l}{\Sigma }_1\\ \\ \mathrm{where}\\ \\ \mathrm{}{\Sigma }_1=\left(\begin{array}{cccc}1& \frac{1}{2}& \frac{1}{3}& \frac{1}{4}\\ \frac{1}{2}& \frac{1}{3}& \frac{1}{4}& \frac{1}{5}\\ \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}\\ \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}\end{array}\right)\end{array}$$

class(X)

ans = 'symmatrix'

Create two symbolic matrix variables with size 2-by-2.

A = symmatrix('A',2)

A =$$A$$

B = symmatrix('B',2)

B =$$B$$

Perform matrix multiplication between A and B. The multiplication of the two symbolic matrix variables is represented by the matrix notation $$\text{A}\text{B}$$.

X = A*B

X =$$A\hspace{0.17em}B$$

Convert the symbolic matrix variable X to a matrix of symbolic scalar variables S. The multiplication of two matrices of symbolic scalar variables is represented by the elements of the matrix product.

S = symmatrix2sym(X)

S =
$$\left(\begin{array}{cc}{A}_{1,1}\hspace{0.17em}{B}_{1,1}+A_{1,2}\hspace{0.17em}{B}_{2,1}& A_{1,1}\hspace{0.17em}{B}_{1,2}+A_{1,2}\hspace{0.17em}{B}_{2,2}\\ A_{2,1}\hspace{0.17em}{B}_{1,1}+A_{2,2}\hspace{0.17em}{B}_{2,1}& A_{2,1}\hspace{0.17em}{B}_{1,2}+A_{2,2}\hspace{0.17em}{B}_{2,2}\end{array}\right)$$