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 …
What is the origin of the determinant in linear algebra?
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 …
How to compute the determinant of a tridiagonal Toeplitz matrix?
The determinant of such a matrix is sometimes called a (generalized) continuant.
Row swap changing sign of determinant - Mathematics Stack …
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 …
What is the importance of determinants in linear algebra?
The determinant being non-zero is equivalent to the matrix being invertible, which is equivalent to the corresponding sets of linear equations having EXACTLY one solution. The determinant …
The relation between trace and determinant of a matrix
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, …
Determinant of a non-square matrix - Mathematics Stack Exchange
I wrote an answer to this question based on determinants, but subsequently deleted it because the OP is interested in non-square matrices, which effectively blocks the use of determinants …
Why does a determinant of $0$ mean the matrix isn't invertible?
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 …
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.