Linked Questions
26 questions linked to/from How to calculate the determinant of all-ones matrix minus the identity?
73
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Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
This question aims to create an "abstract duplicate" of numerous questions that ask about determinants of specific matrices (I may have missed a few):
Characteristic polynomial of a matrix ...
8
votes
4
answers
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Why is the determinant of the all one matrix minus the identity matrix n-1? [duplicate]
Context (skippable)
I was asked (by a friend who is preparing for an exam) whether there was a special trick to compute the determinant of the following matrix. I didn't see anything beyond using the ...
2
votes
3
answers
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Diagonal entries are zero, others are $1$. Find the determinant. [duplicate]
$\det\begin{vmatrix}
0 & \cdots & 1& 1 & 1 \\
\vdots & \ddots & \vdots & \vdots & \vdots \\
1 & \cdots & 1 & 1 & 0
\end{vmatrix}=?$
Attempt:
First I ...
1
vote
2
answers
224
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Calculate $\lvert A \rvert$ if $a_{ij}=0$ if $i=j$ and $1$ otherwise [duplicate]
Let $n$ be a positive integer and let $A=[a_{ij}] \in M_{n\times n} (R)$ be the matrix defined by
$a_{ij}=0$ if $i=j$
$1$ otherwise
To be honest, I've only calculated determinants of matrices ...
3
votes
2
answers
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What is the determinant value of $J-I$ if $I$ is identity matrix and $J=(1)_{101\times 101}$? [duplicate]
Let $J$ be a matrix of order $101\times 101$ which each entry is 1 and suppose $I_{101}$ is identity matrix of order $101\times 101$. The question is : what should be the determinant value of $J-I$ ?
...
1
vote
1
answer
311
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determinant of an $ n\times n$ matrix type [duplicate]
Possible Duplicate:
How to calculate the following determinants
Computing determinant of a specific matrix.
How can one compute the determinant of an $n\times n$ matrix where all the diagonal ...
0
votes
2
answers
159
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Proof explanation about the computation of a certain determinant by Sylvester's theorem [duplicate]
Let $n\geq 2$, $A=[a_{ij}]\in Mat_n(\mathbb{R})$ the matrix defined by $a_{ij}=0$ if $i=j$ and $a_{ij}=1$ if $i\not =j$
Calculate $\det(A)$
Proof:
Sylvester's theorem: https://en.wikipedia.org/...
1
vote
4
answers
124
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Finding determinant of a simple matrix [duplicate]
Can someone please explain how to compute the determinant of $J_n - I_n$ where $j_n$ it a matrix of ones?
E.g. for $n=5$ we get the following matrix
$$\left(\begin{array}{ccccc}
0 & 1 & 1 &...
0
votes
1
answer
52
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Determinant of $12\times12$ matrix [duplicate]
Problem :
Let $A_{12\times12}$=$[a_{ij}]$ satisfies
$$a_{ij}=0\quad (i=j)\\ a_{ij}=1\quad(i\neq j)$$
Evaluate $\det(A)$.
My Attempt
Consider $\det(A+I)$. Since $\det(A+I)=0$, $\lambda = -1$ is ...
41
votes
9
answers
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Determinant of a matrix with diagonal entries $a$ and off-diagonal entries $b$ [duplicate]
I have the following $n\times n$ matrix:
$$A=\begin{bmatrix} a & b & \ldots & b\\ b & a & \ldots & b\\ \vdots & \vdots & \ddots & \vdots\\ b & b & \ldots &...
27
votes
9
answers
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Matrix with zeros on diagonal and ones in other places is invertible
Hi guys I am working with this and I am trying to prove to myself that n by n matrices of the type zero on the diagonal and 1 everywhere else are invertible.
I ran some cases and looked at the ...
14
votes
4
answers
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Determinant of a specific circulant matrix, $A_n$
Let
$$A_2 = \left[ \begin{array}{cc} 0 & 1\\ 1 & 0 \end{array}\right]$$
$$A_3 = \left[ \begin{array}{ccc} 0 & 1 & 1\\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}\right]$$
$$...
10
votes
6
answers
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Determinant of a special skew-symmetric matrix
Simple calculation show that:
$$
\begin{align}
\det(A_2)=\begin{vmatrix}
0& 1 \\
-1& 0
\end{vmatrix}&=1\\
\det(A_4)=\begin{vmatrix}
0& 1 &1 &1 \\
-1&...
7
votes
4
answers
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Determinant of a matrix with $t$ in all off-diagonal entries.
It seems from playing around with small values of $n$ that
$$
\det \left( \begin{array}{ccccc}
-1 & t & t & \dots & t\\
t & -1 & t & \dots & t\\
t & t & -1 &...
3
votes
2
answers
954
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Calculating determinant with different numbers on diagonal and x everywhere else
I'm having troubles solving the following determinant:
$$\left|
\begin{array}{cccc}
a_1 & x & \ldots & x \\
x & a_2 & \ldots & \vdots \\
\vdots & \ldots & ...