Matrix Determinant

Notes

• It's a scalar value that is a function of the entries of a square matrix.

• It represents the area of the parallelogram defined by the vector columns of the matrix.

• If the value is $0$, then:

  • the column vectors are linearly dependent.

• If the value is not $0$, then:

  • the column vectors are linearly independent;
  • the matrix is invertible.

Questions

• In one sentence, shows that $\det(M_1M_2) = \det(M_1)\det(M_2)$.

References

• Wikipedia. Determinant
• 3Blue1Brown. The determinant | Chapter 6, Essence of linear algebra