What's an intuitive way to think about the determinant?
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 …
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 $0$. The free coefficient in the characteristic polynomial of the matrix is $0$. Depending on the …
linear algebra - Why is the determinant zero iff the column vectors …
The determinant of a square matrix is zero if and only if the column vectors are linearly dependent. I see a lot of references to this all over the web, but I can't find an actual …
linear algebra - Show that the determinant of $A$ is equal to the ...
Since this last is a triangular matrix its determinant is the product of the elements in its main diagonal, and we know that in this diagonal appear the eigenvalues of $\;A\;$ so we're done.
linear algebra - Can $\det (A + B)$ be expressed in terms of $\det …
Mar 8, 2024 · It is not perfect but you can get these matrices and do transformations e.g. where matrix pencils are involved (not just characteristic polynomials in one variable, or nonlinear …
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 …
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 …
Are there simple methods for calculating the determinant of …
Oct 13, 2017 · For a $3\times3$ determinant, symmetric or not, there is the fairly simple rule of Sarrus, but there is nothing as simple for larger determinants.
linear algebra - How to find the determinant of a 5x5 matrix ...
Oct 5, 2016 · How to find the determinant of a 5x5 matrix Ask Question Asked 9 years, 3 months ago Modified 4 years, 7 months ago
linear algebra - Help finding the determinant of a 4x4 matrix ...
Jan 4, 2016 · Just for fun, I'll explain a different way of evaluating the determinant. I'm just going to use the relationship between the elementary row/ column operations and the determinant. …