det

Determinant of symbolic matrix

Syntax

``B = det(A)``
``B = det(A,'Algorithm','minor-expansion')``

Description

example

````B = det(A)` returns the determinant of the square matrix `A`.```

example

````B = det(A,'Algorithm','minor-expansion')` uses the minor expansion algorithm to evaluate the determinant of `A`.```

Examples

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Compute the determinant of a symbolic matrix.

```syms a b c d M = [a b; c d]; B = det(M)```
`B = $a d-b c$`

Compute the determinant of a matrix that contain symbolic numbers.

```A = sym([2/3 1/3; 1 1]); B = det(A)```
```B =  $\frac{1}{3}$```

Create a symbolic matrix that contains polynomial entries.

```syms a x A = [1, a*x^2+x, x; 0, a*x, 2; 3*x+2, a*x^2-1, 0]```
```A =  $\left(\begin{array}{ccc}1& a {x}^{2}+x& x\\ 0& a x& 2\\ 3 x+2& a {x}^{2}-1& 0\end{array}\right)$```

Compute the determinant of the matrix using minor expansion.

`B = det(A,'Algorithm','minor-expansion')`
`B = $3 a {x}^{3}+6 {x}^{2}+4 x+2$`

Input Arguments

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Input, specified as a square numeric or symbolic matrix.

Tips

• Matrix computations involving many symbolic variables can be slow. To increase the computational speed, reduce the number of symbolic variables by substituting the given values for some variables.

• The minor expansion method is generally useful to evaluate the determinant of a matrix that contains many symbolic variables. This method is often suited to matrices that contain polynomial entries with multivariate coefficients.

References

[1] Khovanova, T. and Z. Scully. "Efficient Calculation of Determinants of Symbolic Matrices with Many Variables." arXiv preprint arXiv:1304.4691 (2013).

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