# Tagged Questions

Question about determinants, computation or theory. If $E$ is a vector space of dimension $d$, then we can compute the determinant of a $d$-uple $(v_1,\ldots,v_d)$ with respect to a basis.

45 views

### Algorithm for finding the value of determinant

Okay I am writing to write a program which computes the determinant of a matrix. So is there an algorithm that allows you to do that ? Are there any other ways of finding the determinant value other ...
358 views

### Why is determinant a multilinear function?

I am trying to understand (intuitive explanation will be fine) why determinant is a multilinear function and therefore to learn how elementary row operation affect the determinant. I understand that ...
42 views

### Alternating multilinear function satisfies $f(A)=\det(A)f(Id)$

I've just seen a proof of the statement: "Given $\alpha$ in a commutative ring $K$ there is a unique alternating multilinear function $f$ with $f(Id)=\alpha$." The determinant is defined as the ...
42 views

### Prove that det($A$) is non-zero iff $A$ is row equivalent to the $n\times n$ identity matrix

$A$ is an $n\times n$ matrix. Now if the row-reduced echelon form for this $A$ is $E$ then after all the row operations we have $\det(A)=M\det(E)$ where $M$ is a non-zero ...
49 views

### Integration of exponential matrix and determinant?

Is it possible to prove $$\int \exp\{-\frac{1}{2}(\beta-\hat\beta)^T(X^TH^{-1}X)(\beta-\hat\beta)\}\text{d}\beta=\{\det(X^TH^{-1}X)\}^{-1/2},$$ where $\hat\beta,X,H$ are all known? What additional ...
64 views

### What is $\mid\text{det}(A,G)\mid$?

I am reading an old paper dated back in 70', where I encounter this $$\mid\text{det}(A,G)\mid=(\text{det}\{(A,G)'(A,G)\})^{\frac{1}{2}}.$$ We compute the determinant of a single matrix, don't we? ...
131 views

### How to prove that this matrix is total unimodular

This matrix is total unimodular (tested by a computer program). ...
84 views

### relation between special linear group and special orthogonal group

What is the difference between special linear group and special orthogonal group ? The special linear group is the set of endomorphisms with determinant $1$. On the other hand, the special ...
56 views

### Find $a$ in the following matrix

I have the following question : matrix $A$ isn't diagonalizable while $a \in R$ $$A = \begin{pmatrix} 3 & 0 & 0 \\ 0 & a & a-2 \\ 0 & -2 & 0 \end{pmatrix}$$ Find $a$. I don'...
154 views

Let $S$ and $A$ be a symmetric and a skew-symmetric $n \times n$ matrix over $\mathbb{R}$, respectively. When calculating (numerically) the product $S^{-1} A S^{-1}$ I keep getting the factor $\det S$ ...
82 views

37 views

34 views

19 views