Give an example of a skew–symmetric2×2–matrix B with entries in C for which I2+B is not invertible...
Give an example of a skew-symmetric $2times2$ matrix $B$ with entries in $mathbb C$ for which $I_2+B$ is not invertible.
I'm struggling with this Lin Algebra problem if you could help me with it that'd be great. Thank you.
linear-algebra matrices examples-counterexamples
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
asked Nov 30 at 16:50
Konstantin Uvarov
1
closed as off-topic by GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus Dec 2 at 0:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Give an example of a skew-symmetric $2times2$ matrix $B$ with entries in $mathbb C$ for which $I_2+B$ is not invertible.
I'm struggling with this Lin Algebra problem if you could help me with it that'd be great. Thank you.
linear-algebra matrices examples-counterexamples
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
asked Nov 30 at 16:50
Konstantin Uvarov
1
closed as off-topic by GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus Dec 2 at 0:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
The condition that B is 2×2 confines the scale of this problem, whereas the restriction that B is skew-symmetric transform it into a single-variable problem. Please show us your work.
– GNUSupporter 8964民主女神 地下教會
Nov 30 at 16:56
add a comment |
Give an example of a skew-symmetric $2times2$ matrix $B$ with entries in $mathbb C$ for which $I_2+B$ is not invertible.
I'm struggling with this Lin Algebra problem if you could help me with it that'd be great. Thank you.
linear-algebra matrices examples-counterexamples
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
asked Nov 30 at 16:50
Konstantin Uvarov
1
Give an example of a skew-symmetric $2times2$ matrix $B$ with entries in $mathbb C$ for which $I_2+B$ is not invertible.
I'm struggling with this Lin Algebra problem if you could help me with it that'd be great. Thank you.
linear-algebra matrices examples-counterexamples
linear-algebra matrices examples-counterexamples
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
asked Nov 30 at 16:50
Konstantin Uvarov
1
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
asked Nov 30 at 16:50
Konstantin Uvarov
1
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
edited Dec 1 at 11:06
Martin Sleziak
44.6k7115270
44.6k7115270
asked Nov 30 at 16:50
Konstantin Uvarov
1
asked Nov 30 at 16:50
Konstantin Uvarov
1
asked Nov 30 at 16:50
Konstantin Uvarov
1
1
closed as off-topic by GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus Dec 2 at 0:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus Dec 2 at 0:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, user1551, Brahadeesh, Rebellos, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.
The condition that B is 2×2 confines the scale of this problem, whereas the restriction that B is skew-symmetric transform it into a single-variable problem. Please show us your work.
– GNUSupporter 8964民主女神 地下教會
Nov 30 at 16:56
add a comment |
The condition that B is 2×2 confines the scale of this problem, whereas the restriction that B is skew-symmetric transform it into a single-variable problem. Please show us your work.
– GNUSupporter 8964民主女神 地下教會
Nov 30 at 16:56
The condition that B is 2×2 confines the scale of this problem, whereas the restriction that B is skew-symmetric transform it into a single-variable problem. Please show us your work.
– GNUSupporter 8964民主女神 地下教會
Nov 30 at 16:56
The condition that B is 2×2 confines the scale of this problem, whereas the restriction that B is skew-symmetric transform it into a single-variable problem. Please show us your work.
– GNUSupporter 8964民主女神 地下教會
Nov 30 at 16:56
add a comment |
2 Answers
2
active
oldest
votes
You need to put two concepts together: 1. what is a skew symmetric matrix? and 2. When is a matrix not invertible? The answer for 1 is a matrix of type $$B=begin{pmatrix}0 &b\ -b&0end{pmatrix}$$
The answer for 2 is $$det(I_2+B)=0$$
Calculate explicitly this determinant, and see when it is $0$.
answered Nov 30 at 16:58
Andrei
10.9k21025
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
add a comment |
Hints: (1) A skew symmetric $2times 2$ matrix has entries $a,b,-b,a$
(2) $I_2$ has entries $1,0,0,1$
(3) A square matrix is not invertible if and only if its determinant is zero
answered Nov 30 at 16:54
MPW
29.8k11956
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
You need to put two concepts together: 1. what is a skew symmetric matrix? and 2. When is a matrix not invertible? The answer for 1 is a matrix of type $$B=begin{pmatrix}0 &b\ -b&0end{pmatrix}$$
The answer for 2 is $$det(I_2+B)=0$$
Calculate explicitly this determinant, and see when it is $0$.
answered Nov 30 at 16:58
Andrei
10.9k21025
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
add a comment |
You need to put two concepts together: 1. what is a skew symmetric matrix? and 2. When is a matrix not invertible? The answer for 1 is a matrix of type $$B=begin{pmatrix}0 &b\ -b&0end{pmatrix}$$
The answer for 2 is $$det(I_2+B)=0$$
Calculate explicitly this determinant, and see when it is $0$.
answered Nov 30 at 16:58
Andrei
10.9k21025
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
add a comment |
You need to put two concepts together: 1. what is a skew symmetric matrix? and 2. When is a matrix not invertible? The answer for 1 is a matrix of type $$B=begin{pmatrix}0 &b\ -b&0end{pmatrix}$$
The answer for 2 is $$det(I_2+B)=0$$
Calculate explicitly this determinant, and see when it is $0$.
answered Nov 30 at 16:58
Andrei
10.9k21025
You need to put two concepts together: 1. what is a skew symmetric matrix? and 2. When is a matrix not invertible? The answer for 1 is a matrix of type $$B=begin{pmatrix}0 &b\ -b&0end{pmatrix}$$
The answer for 2 is $$det(I_2+B)=0$$
Calculate explicitly this determinant, and see when it is $0$.
answered Nov 30 at 16:58
Andrei
10.9k21025
answered Nov 30 at 16:58
Andrei
10.9k21025
answered Nov 30 at 16:58
Andrei
10.9k21025
answered Nov 30 at 16:58
Andrei
10.9k21025
10.9k21025
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
add a comment |
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
+1 for stating more clearly what I intended.
– MPW
Nov 30 at 17:05
add a comment |
Hints: (1) A skew symmetric $2times 2$ matrix has entries $a,b,-b,a$
(2) $I_2$ has entries $1,0,0,1$
(3) A square matrix is not invertible if and only if its determinant is zero
answered Nov 30 at 16:54
MPW
29.8k11956
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
add a comment |
Hints: (1) A skew symmetric $2times 2$ matrix has entries $a,b,-b,a$
(2) $I_2$ has entries $1,0,0,1$
(3) A square matrix is not invertible if and only if its determinant is zero
answered Nov 30 at 16:54
MPW
29.8k11956
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
add a comment |
Hints: (1) A skew symmetric $2times 2$ matrix has entries $a,b,-b,a$
(2) $I_2$ has entries $1,0,0,1$
(3) A square matrix is not invertible if and only if its determinant is zero
answered Nov 30 at 16:54
MPW
29.8k11956
Hints: (1) A skew symmetric $2times 2$ matrix has entries $a,b,-b,a$
(2) $I_2$ has entries $1,0,0,1$
(3) A square matrix is not invertible if and only if its determinant is zero
answered Nov 30 at 16:54
MPW
29.8k11956
edited Nov 30 at 17:03
answered Nov 30 at 16:54
MPW
29.8k11956
answered Nov 30 at 16:54
MPW
29.8k11956
answered Nov 30 at 16:54
MPW
29.8k11956
29.8k11956
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
add a comment |
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
I thought that skew symmetric matrices have $A_{ij}=-A_{ji}$, therefore $A_{ii}=0$
– Andrei
Nov 30 at 16:59
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
@Andrei : Yes, that's true. So always $a=0$. Hmm, I see I have listed the entries in the wrong order, my bad, will correct. Thanks.
– MPW
Nov 30 at 17:03
add a comment |
The condition that B is 2×2 confines the scale of this problem, whereas the restriction that B is skew-symmetric transform it into a single-variable problem. Please show us your work.
– GNUSupporter 8964民主女神 地下教會
Nov 30 at 16:56