# symmatrix2sym

Convert symbolic matrix variable to array of scalar variables

## Syntax

``S = symmatrix2sym(M)``

## Description

example

````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

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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 ```

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

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 = ${‖A‖}_{2}$`
`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 = $\sqrt{{|{A}_{1,1}|}^{2}+{|{A}_{1,2}|}^{2}+{|{A}_{1,3}|}^{2}}$`
`class(N)`
```ans = 'sym' ```

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 = ${A}^{\mathrm{T}} B$`

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 = $\left(\begin{array}{c}{A}_{1} {B}_{1}+{A}_{2} {B}_{2}+{A}_{3} {B}_{3}\end{array}\right)$`

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

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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`.

Introduced in R2021a

## Support

#### Mathematical Modeling with Symbolic Math Toolbox

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