min

Create a symbolic vector of real elements. Find the smallest real element using the symbolic min function.

syms x real
A = [23 42 37 18 x];
M = min(A)

M = $$\min \left(\left[18,x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)$$

The symbolic min function returns an unevaluated expression. The expression excludes elements in A that do not represent minimum values.

Create a symbolic vector and compute its minimum, excluding NaN values.

syms x positive
A = [1.75 x 3.25 -2.5 NaN 0.5 NaN 0.2 -4*x];
M = min(A,[],"omitnan")

M = 
$$\min \left(\left[-\frac{5}{2},-4\hspace{0.17em}x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)$$

min(A) also produces this result because "omitnan" is the default option.

Use the "includenan" option to return NaN.

M = min(A,[],"includenan")

M = $$\mathrm{NaN}$$

Create a symbolic matrix and find the smallest element in each column.

syms x real
A = [1 x -0.5; -2 1 x]

A = 
$$\left(\begin{array}{ccc}1& x& -\frac{1}{2}\\ -2& 1& x\end{array}\right)$$

M = min(A)

M = 
$$\left(\begin{array}{ccc}-2& \min \left(\left[1,x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)& \min \left(\left[-\frac{1}{2},x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)\end{array}\right)$$

Create a symbolic matrix and find the smallest element in each row.

syms x real
A = [1 x -0.5; -2 1 x]

A = 
$$\left(\begin{array}{ccc}1& x& -\frac{1}{2}\\ -2& 1& x\end{array}\right)$$

M = min(A,[],2)

M = 
$$\left(\begin{array}{c}\min \left(\left[-\frac{1}{2},x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)\\ \min \left(\left[-2,x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)\end{array}\right)$$

Create a symbolic matrix A. Find the smallest elements in each row of A and return the column indices corresponding to the first occurrence of the minimum value in each row. Because A contains a symbolic variable x with an undetermined value, min cannot explicitly evaluate the minimum value in each row and returns the indices as -1.

syms x real
A = [1 x -0.5; -2 2 x]

A = 
$$\left(\begin{array}{ccc}1& x& -\frac{1}{2}\\ -2& 2& x\end{array}\right)$$

[M,I] = min(A,[],2)

M = 
$$\left(\begin{array}{c}\min \left(\left[-\frac{1}{2},x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)\\ \min \left(\left[-2,x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)\end{array}\right)$$

I = 2×1

    -1
    -1

Substitute a symbolic number for the variable x in the symbolic matrix A. Find the smallest elements in each row again. Here, min is able to evaluate the minimum values and returns the column indices corresponding to the first occurrence of the minimum value in each row.

A = subs(A,x,sqrt(2))

A = 
$$\left(\begin{array}{ccc}1& \sqrt{2}& -\frac{1}{2}\\ -2& 2& \sqrt{2}\end{array}\right)$$

[M,I] = min(A,[],2)

M = 
$$\left(\begin{array}{c}-\frac{1}{2}\\ -2\end{array}\right)$$

I = 2×1

     3
     1

Create a symbolic matrix. Find the minimum over all dimensions of the matrix by using the min function with the "all" option.

syms x real
A = [1 x -0.5; -2 1 x]

A = 
$$\left(\begin{array}{ccc}1& x& -\frac{1}{2}\\ -2& 1& x\end{array}\right)$$

M = min(A,[],"all")

M = $$\min \left(\left[-2,x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)$$

Create two symbolic matrices with complex elements. Find the smallest elements taken from the two matrices. The largest elements are the complex values with the smallest magnitude.

syms x y
A = [x 2+1i; 3 4i; -5 y]

A = 
$$\left(\begin{array}{cc}x& 2+\mathrm{i}\\ 3& 4\hspace{0.17em}\mathrm{i}\\ -5& y\end{array}\right)$$

B = [1 y; 2i 1+1i; -3 x]

B = 
$$\left(\begin{array}{cc}1& y\\ 2\hspace{0.17em}\mathrm{i}& 1+\mathrm{i}\\ -3& x\end{array}\right)$$

C = min(A,B)

C = 
$$\left(\begin{array}{cc}\min \left(\left[1,x\right],\left[\right],2,\mathrm{"omitnan"},x\notin \mathbb{R}\right)& \min \left(\left[2+\mathrm{i},y\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symtrue}\right)\\ 2\hspace{0.17em}\mathrm{i}& 1+\mathrm{i}\\ -3& \min \left(\left[x,y\right],\left[\right],2,\mathrm{"omitnan"},x\notin \mathbb{R}\vee y\notin \mathbb{R}\right)\end{array}\right)$$

Define the following expression by using the symbolic min function. Assume that the variable $$x$$ is real.

syms x real
f(x) = sqrt(1 - min(x,1))

f(x) = $$\sqrt{1-\min \left(\left[1,x\right],\left[\right],2,\mathrm{"omitnan"},\mathrm{symfalse}\right)}$$

Plot the expression by using fplot.

fplot(f,[-5 5])