Tagged Questions
0
votes
1answer
26 views
proof about deteminant of a complex linear transformation
say I have a linear space $V$ over $\Bbb C$ and a linear transformation $T:V \to V$
such that $T=A+iB$ where $A,B \in \Bbb R^{n \times n}$
I proved already that $T_\Bbb R = \begin{pmatrix} A & -B ...
1
vote
2answers
59 views
deteminant of a block skew-symmetric matrix
If I have a matrix if the form \begin{pmatrix} A & -B \\ B & A \end{pmatrix}
how do i turn it into something like \begin{pmatrix} X & Y \\ 0 & Z \end{pmatrix}
so the determinant is ...
5
votes
5answers
136 views
How to prove that $\det(M) = (-1)^k \det(A) \det(B)?$
Let $\mathbf{A}$ and $\mathbf{B}$ be $k \times k$ matrices and $\mathbf{M}$ is the block matrix
$$\mathbf{M} = \begin{pmatrix}0 & \mathbf{B} \\ \mathbf{A} & 0\end{pmatrix}.$$
How to prove that ...
3
votes
1answer
60 views
Fast way to calculate determinant for a block matrix
I have a block matrix
$$Q_{(n+m-1)\times(n+m-1)} = \begin{pmatrix} A & -J\\-J^t & B \end{pmatrix}$$
where
$$A_{(m-1)\times(m-1)} = n*I_{(m-1)\times(m-1)} \text{ and } B_{n\times n} = ...
0
votes
2answers
69 views
Linear algebra: need help with proof
Can someone please help me with this proof.
For $A,B$ ∈ $F^{n×n}$, show that $AB$ and $BA$ have the same characteristic polynomial.
0
votes
2answers
93 views
How do I write this matrix in Jordan-Normal Form
I have the matrix $A=\begin{pmatrix}2&2&1\\-1&0&1\\4&1&-1\end{pmatrix}$, I want to write it in Jordan-Normal Form. I have $x_1=3,x_2=x_3=-1$ and calculated eigenvectors ...
0
votes
4answers
68 views
Determinant of a $4\times4$ matrice with one unknown?
I have to calculate the determinant of this matrice. I want to use the rule of sarrus, but this does only work with a $3\times3$ matrice:
$$
A=
\begin{bmatrix}
1 & -2 & -6 & u \\
...
5
votes
3answers
335 views
Determinants of block matrices
Let $A,B \in \mathbb{R}^{n,n}$.
Now $C = \begin{pmatrix} A & iB \\ -iB & A \end{pmatrix}$ and $D = \begin{pmatrix} A & B \\ -B & A \end{pmatrix}$.
Show that $\det(C) \in \mathbb{R}$ ...
2
votes
0answers
77 views
Determinant, number of non zero columns
Trying to build a reduction from the maximum coverage problem to my research problem, I'm facing this difficulty :
Let $X$ be a $n \times m$ binary matrix (with $m > n$), can we define a square ...
