symmatrix2sym

Convert symbolic matrix variable to array of scalar variables

Since R2021a

Syntax

S = symmatrix2sym(M)

Description

S = symmatrix2sym(M) converts a symbolic matrix variable M of type symmatrix to an array of symbolic scalar variables S of type sym.

The output array is the same size as the input symbolic matrix variable and its components are filled with automatically generated elements. For example, syms M [1 3] matrix; S = symmatrix2sym(M) creates the matrix S = [M1_1, M1_2, M1_3]. The generated elements M1_1, M1_2, and M1_3 do not appear in the MATLAB^® workspace.

Examples

Convert Addition of Two Matrices

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.

syms A B [2 3] matrix
A

A = $$A$$

B

B = $$B$$

Add the two matrices. The result is represented by the matrix notation $$\text{A}+\text{B}$$.

X = A + B

X = $$A+B$$

The data type of X is symmatrix.

class(X)

ans = 
'symmatrix'

Convert the symbolic matrix variable X to a matrix of symbolic scalar variables Y. The result is denoted by the sum of the matrix components.

Y = symmatrix2sym(X)

Y = 
$$\left(\begin{array}{ccc}{A}_{1,1}+B_{1,1}& A_{1,2}+B_{1,2}& A_{1,3}+B_{1,3}\\ A_{2,1}+B_{2,1}& A_{2,2}+B_{2,2}& A_{2,3}+B_{2,3}\end{array}\right)$$

The data type of Y is sym.

class(Y)

ans = 
'sym'

Show that the converted result in Y is equal to the sum of two matrices of symbolic scalar variables.

syms A B [2 3]
Y2 = A + B

Y2 = 
$$\left(\begin{array}{ccc}{A}_{1,1}+B_{1,1}& A_{1,2}+B_{1,2}& A_{1,3}+B_{1,3}\\ A_{2,1}+B_{2,1}& A_{2,2}+B_{2,2}& A_{2,3}+B_{2,3}\end{array}\right)$$

isequal(Y,Y2)

ans = logical
   1

Convert Hessian Matrix

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

syms A [3 3] matrix
syms X [3 1] matrix

Find the Hessian matrix of $${\text{X}}^T\text{A}\text{X}$$.

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

H = $$A^{\mathrm{T}}+A$$

Convert the result from a symbolic matrix variable H to a matrix of symbolic scalar variables S.

S = symmatrix2sym(H)

S = 
$$\left(\begin{array}{ccc}2\hspace{0.17em}{A}_{1,1}& A_{1,2}+A_{2,1}& A_{1,3}+A_{3,1}\\ A_{1,2}+A_{2,1}& 2\hspace{0.17em}{A}_{2,2}& A_{2,3}+A_{3,2}\\ A_{1,3}+A_{3,1}& A_{2,3}+A_{3,2}& 2\hspace{0.17em}{A}_{3,3}\end{array}\right)$$

Find Two-Norm of Vector

Create a 1-by-3 symbolic matrix variable that represents a vector.

syms A [1 3] matrix

Find the 2-norm of the vector A. The result is a symbolic matrix variable with symmatrix data type.

N = norm(A)

N = $${\Vert A\Vert }_2$$

class(N)

ans = 
'symmatrix'

Convert N to a symbolic scalar variable to express the 2-norm in terms of the components of A. The result is a symbolic scalar variable with sym data type.

N = symmatrix2sym(N)

N = 
$$\sqrt{{\left|A_{1,1}\right|}^2+{\left|A_{1,2}\right|}^2+{\left|A_{1,3}\right|}^2}$$

class(N)

ans = 
'sym'

Find Dot Product of Two Vectors

Create two vectors of size 3-by-1 as symbolic matrix variables.

syms A B [3 1] matrix

Find the dot product of the two vectors by evaluating transpose(A)*B.

C = transpose(A)*B

C = $$A^{\mathrm{T}}\hspace{0.17em}B$$

Convert C to a symbolic scalar variable to express the dot product in terms of the components of A and B.

C = symmatrix2sym(C)

C = $$A_1\hspace{0.17em}{B}_1+A_2\hspace{0.17em}{B}_2+A_3\hspace{0.17em}{B}_3$$

Concatenate Two Matrices

Create two 2-by-3 symbolic matrix variables.

syms A B [2 3] matrix

Concatenate the two matrices vertically using the command vertcat(A,B) or [A; B].

C = [A; B]

C = 
$$\left(\begin{array}{c}A\\ B\end{array}\right)$$

Convert C to a matrix of symbolic scalar variables.

C = symmatrix2sym(C)

C = 
$$\left(\begin{array}{ccc}{A}_{1,1}& A_{1,2}& A_{1,3}\\ A_{2,1}& A_{2,2}& A_{2,3}\\ B_{1,1}& B_{1,2}& B_{1,3}\\ B_{2,1}& B_{2,2}& B_{2,3}\end{array}\right)$$

Input Arguments

M — Input

symbolic matrix variable

Input, specified as a symbolic matrix variable.

Data Types: symmatrix

Tips

• To show all the functions in Symbolic Math Toolbox™ that accept symbolic matrix variables as input, use the command methods symmatrix.

• Instead of using symmatrix2sym to convert a symbolic matrix variable to an array of symbolic scalar variables, you can use the shortcut sym. For an example, see Convert Hessian Matrix. (since R2022b)

Version History

Introduced in R2021a