What's an intuitive way to think about the determinant?
The first thing to think about if you want an “abstract” definition of the determinant to unify all those others is that it’s not an array of numbers with bars on the side. What we’re really looking for is a …
What is the real meaning of the determinant of a matrix?
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 rows of …
Determinant of large matrices: it must exist a faster way
May 7, 2017 · Now the matrix is upper-triangular, and so the determinant is just the product of the diagonal entries. So we have $$ \det A = -6 (-4 \times 1 \times -4) = -96 $$ So there you have it: …
What does it mean to have a determinant equal to zero?
Nov 27, 2019 · The determinant of the linear transformation determined by the matrix is 0 0. The free coefficient in the characteristic polynomial of the matrix is 0 0. Depending on the definition of the …
linear algebra - How to find the determinant of a 5x5 matrix ...
Oct 6, 2016 · How to find the determinant of a 5x5 matrix Ask Question Asked 9 years, 3 months ago Modified 4 years, 7 months ago
Proving the formula for finding the determinant of a square matrix.
Similarly, the formula for the determinant of an n × n n × n matrix is not given in my textbook. Unfortunately, I can't seem to find a proof that I could comprehend on the internet. It would be great if …
Using Cholesky decomposition to compute covariance matrix …
Mar 22, 2019 · What does "computing the determinant directly" mean in this context? If you are using a library, the routine to compute determinants might well be using something like Gaussian elimination …
How to find the determinant of this $6\\times 6$ X-matrix?
Aug 9, 2020 · Usually using row operations will help in reducing the determinant to something that is more manageable (like diagonal or upper triangular matrices). You should know how the row …
The relation between trace and determinant of a matrix
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, then its eigenvalues are …
Why does a determinant of $0$ mean the matrix isn't invertible?
I always got taught that if the determinant of a matrix is 0 0 then the matrix isn't invertible, but why is that? My flawed attempt at understanding things: This approaches the subject from a geometric point …