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Recent questions tagged eigen-value
3
votes
1
answer
151
Eigen values
The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is A). $\pm i$ B), $(\pm i,\pm1)$ C). $\pm1$ D). $(0,\pm i)$
Himanshu1
asked
in
Linear Algebra
Dec 26, 2015
by
Himanshu1
1.4k
views
eigen-value
engineering-mathematics
linear-algebra
1
vote
0
answers
152
TIFR-2015-Maths-A-3
Let $A$ be a $10 \times 10$ matrix with complex entries such that all its eigenvalues are non-negative real numbers, and at least one eigenvalue is positive. Which of the following statements is always false ? There exists a matrix $B$ such that $AB-BA = B$ There exists a ... $AB-BA = A$ There exists a matrix $B$ such that $AB+BA=A$ There exists a matrix $B$ such that $AB+BA=B$
makhdoom ghaya
asked
in
Linear Algebra
Dec 19, 2015
by
makhdoom ghaya
408
views
tifrmaths2015
linear-algebra
matrix
eigen-value
1
vote
1
answer
153
TIFR-2014-Maths-A-9
Let $A(\theta)=\begin{pmatrix} \cos \theta& \sin \theta \\ -\sin \theta& \cos \theta \end{pmatrix}$, where $\theta \in (0, 2\pi)$. Mark the correct statement below. $A(\theta)$ has eigenvectors in $\mathbb{R}^2$ for all $θ \in (0, 2\pi)$ $A(\theta)$ does not ... $θ \in (0, 2\pi)$ $A(\theta)$ has eigenvectors in $\mathbb{R}^2$ , for exactly $2$ values of $θ \in (0, 2\pi)$
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
367
views
tifrmaths2014
linear-algebra
matrix
eigen-value
4
votes
3
answers
154
eigen value
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is 1) $18.33$ 2) $-18.33$ 3) $18.33-9.33 i$ 4) $18.33+9.33i$
Pooja Palod
asked
in
Linear Algebra
Dec 16, 2015
by
Pooja Palod
816
views
engineering-mathematics
eigen-value
2
votes
1
answer
155
Eigen Vector
The linear operation $L(x)$ is defined by the cross product $L(x)=b \times x$, where $b=\begin{bmatrix} 0 &1 & 0 \end{bmatrix}^T$ and $x=\begin{bmatrix} x_1 &x_2 & x_3 \end{bmatrix}^T$ are three dimensional vectors. The $3 \times 3$ matrix $M$ ... of $M$ are (A) $0,+1,-1$ (B) $1,-1,1$ (C) $i,-i,1$ (D) $i,-i,0$ how to solve this..??
Abhishekcs10
asked
in
Linear Algebra
Dec 16, 2015
by
Abhishekcs10
2.1k
views
eigen-value
linear-algebra
4
votes
1
answer
156
TIFR-2011-Maths-A-3
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ has An eigenvalue which is purely imaginary At least one real eigenvalue At least two eigenvalues which are not real At least $2$ distinct real eigenvalues
makhdoom ghaya
asked
in
Linear Algebra
Dec 9, 2015
by
makhdoom ghaya
986
views
tifrmaths2011
linear-algebra
matrix
eigen-value
3
votes
2
answers
157
1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.
yes
asked
in
Linear Algebra
Oct 21, 2015
by
yes
5.1k
views
linear-algebra
eigen-value
5
votes
2
answers
158
TIFR2010-Maths-A-10
Let $M_{n}(R)$ be the set of n x n matrices with real entries. Which of the following statements is true? Any matrix $A \in M_{4}(R)$ has a real eigenvalue Any matrix $A \in M_{5}(R)$ has a real eigenvalue Any matrix $A \in M_{2}(R)$ has a real eigenvalue None of the above
makhdoom ghaya
asked
in
Linear Algebra
Oct 11, 2015
by
makhdoom ghaya
774
views
tifrmaths2010
eigen-value
27
votes
6
answers
159
GATE CSE 2015 Set 3 | Question: 15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ ... $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$
go_editor
asked
in
Linear Algebra
Feb 14, 2015
by
go_editor
12.9k
views
gatecse-2015-set3
linear-algebra
eigen-value
normal
24
votes
4
answers
160
GATE CSE 2015 Set 1 | Question: 36
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the values of $a$ and $b$? $\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$ $a = 6, b = 4$ $a = 4, b = 6$ $a = 3, b = 5$ $a = 5, b = 3 $
makhdoom ghaya
asked
in
Linear Algebra
Feb 13, 2015
by
makhdoom ghaya
4.9k
views
gatecse-2015-set1
linear-algebra
eigen-value
normal
20
votes
3
answers
161
GATE CSE 2015 Set 2 | Question: 5
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
go_editor
asked
in
Linear Algebra
Feb 12, 2015
by
go_editor
5.7k
views
gatecse-2015-set2
linear-algebra
eigen-value
easy
numerical-answers
22
votes
8
answers
162
GATE IT 2006 | Question: 26
What are the eigenvalues of the matrix $P$ given below $P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$ $a, a -√2, a + √2$ $a, a, a$ $0, a, 2a$ $-a, 2a, 2a$
Ishrat Jahan
asked
in
Linear Algebra
Oct 31, 2014
by
Ishrat Jahan
5.2k
views
gateit-2006
linear-algebra
eigen-value
normal
50
votes
7
answers
163
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Ishrat Jahan
asked
in
Linear Algebra
Oct 30, 2014
by
Ishrat Jahan
11.4k
views
gateit-2007
linear-algebra
eigen-value
normal
22
votes
4
answers
164
GATE CSE 2011 | Question: 40
Consider the matrix as given below. $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? $1, 4, 3$ $3, 7, 3$ $7, 3, 2$ $1, 2, 3$
go_editor
asked
in
Linear Algebra
Sep 29, 2014
by
go_editor
3.7k
views
gatecse-2011
linear-algebra
eigen-value
easy
34
votes
3
answers
165
GATE CSE 2014 Set 3 | Question: 4
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is ... eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
go_editor
asked
in
Linear Algebra
Sep 28, 2014
by
go_editor
8.8k
views
gatecse-2014-set3
linear-algebra
eigen-value
normal
78
votes
9
answers
166
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
go_editor
asked
in
Linear Algebra
Sep 28, 2014
by
go_editor
28.5k
views
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
47
votes
4
answers
167
GATE CSE 2014 Set 1 | Question: 5
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
go_editor
asked
in
Linear Algebra
Sep 26, 2014
by
go_editor
10.8k
views
gatecse-2014-set1
linear-algebra
eigen-value
numerical-answers
normal
15
votes
3
answers
168
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$ $-1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $-1$
gatecse
asked
in
Linear Algebra
Sep 21, 2014
by
gatecse
4.5k
views
gatecse-2005
linear-algebra
eigen-value
easy
19
votes
2
answers
169
GATE CSE 2010 | Question: 29
Consider the following matrix $A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$ If the eigenvalues of A are $4$ and $8$, then $x = 4$, $y = 10$ $x = 5$, $y = 8$ $x = 3$, $y = 9$ $x = -4$, $y =10$
gatecse
asked
in
Linear Algebra
Sep 21, 2014
by
gatecse
6.7k
views
gatecse-2010
linear-algebra
eigen-value
easy
25
votes
5
answers
170
GATE CSE 2002 | Question: 5a
Obtain the eigen values of the matrix$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$
Kathleen
asked
in
Linear Algebra
Sep 16, 2014
by
Kathleen
3.1k
views
gatecse-2002
linear-algebra
eigen-value
normal
descriptive
32
votes
6
answers
171
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
Kathleen
asked
in
Linear Algebra
Sep 13, 2014
by
Kathleen
7.9k
views
gate1993
eigen-value
linear-algebra
easy
multiple-selects
26
votes
3
answers
172
GATE CSE 2008 | Question: 28
How many of the following matrices have an eigenvalue 1? $\left[\begin{array}{cc}1 & 0 \\0 & 0 \end{array} \right]\left[\begin{array}{cc}0 & 1 \\0 & 0 \end{array} \right] \left[\begin{array}{cc}1 & -1 \\1 & 1 \end{array} \right]$ and $\left[\begin{array}{cc}-1 & 0 \\1 & -1 \end{array} \right]$ one two three four
Kathleen
asked
in
Linear Algebra
Sep 12, 2014
by
Kathleen
6.1k
views
gatecse-2008
eigen-value
linear-algebra
63
votes
4
answers
173
GATE CSE 2007 | Question: 25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$
priya
asked
in
Linear Algebra
Sep 2, 2014
by
priya
11.9k
views
gatecse-2007
eigen-value
linear-algebra
difficult
29
votes
5
answers
174
GATE CSE 2012 | Question: 11
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
gatecse
asked
in
Linear Algebra
Aug 5, 2014
by
gatecse
8.7k
views
gatecse-2012
linear-algebra
eigen-value
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