What is determinant?

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 Determinant

The determinant of a matrix is a special number that can be calculated from a square matrix.

A matrix is an array of numbers:

What is it for?

The determinant helps us find the inverse of a matrix, tells us things about the matrix that are useful in systems of linear equations, calculus and more.

 Symbol:

 The symbol for determinant is two vertical lines either side.

 Example:

|A| means the determinant of the matrix A

Properties of determinant

Reflection Property

All-zero Property

Proportionality Property

Switching Property

Triangle Property

Scalar Multiple Property

Sum Property

Applications

Linear independence

Vandermonde determinant

Orientation of a basis

Volume and Jacobian determinant





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