The determinant of the linear transformation (matrix) T is the signed volume of the region gotten by applying T to the unit cube. (Don’t worry too much if you don’t know what the “signed” part …

3 I always got taught that if the determinant of a matrix is $0$ then the matrix isn't invertible, but why is that? My flawed attempt at understanding things: This approaches the subject from a …

Oct 21, 2016 · We often learn in a standard linear algebra course that a determinant is a number associated with a square matrix. We can define the determinant also by saying that it is the …

Oct 5, 2016 · How to find the determinant of a 5x5 matrix Ask Question Asked 9 years, 2 months ago Modified 4 years, 6 months ago

Sep 29, 2015 · If determinant of a matrix is zero, it means that area of the parallelogram in the transformed space is zero. Means if you apply the matrix which has determinant zero, it will …

Apr 16, 2017 · Insightful proofs for Sherman-Morrison Formula and Matrix Determinant Lemma Ask Question Asked 13 years ago Modified 2 years, 7 months ago

All of the following ideas are connected to each other; 1- Swapping any 2 rows of a matrix, flips the sign of its determinant. 2- The determinant of product of 2 matrices is equal to the product …

Mar 30, 2015 · The absolute value of the determinant of a matrix is the volume of the parallepiped spanned by the vectors in the matrix. Parallelpiped is the 3d version of a parallelogram. The …

However when it comes to a $3 \times 3$ matrix, all the sources that I have read purely state that the determinant of a $3 \times 3$ matrix defined as a formula (omitted here, basically it's …

Jan 4, 2017 · The determinant and the trace are two quite different beasts, little relation can be found among them. If the matrix is not only symmetric (hermitic) but also positive semi-definite, …