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Recent questions tagged eigen-value

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91

Na462 asked in Linear Algebra Nov 7, 2018

by Na462

1.8k views

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92

Na462 asked in Linear Algebra Oct 26, 2018

by Na462

500 views

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93

Eigen Values(Matrix is not idempotent)
Given that a matrix $A_{3\times3},$which is not idempotent matrix.And $A^{3}=A.$ Then find them, $1)$ Eigen Values $2)$ Trace of the matrix$=$Sum of Leading Diagonal Elements$=\sum a_{ij},$ where $i=j$ $3)Det(A)$

Lakshman Bhaiya asked in Linear Algebra Oct 25, 2018

by Lakshman Bhaiya

487 views

0 votes

0 answers

94

Linear algebra
Given that the matrix $A=\begin{bmatrix} a_{11} &a_{12} \\ a_{21} &a_{22} \end{bmatrix}$ and Eigen value are $1,-2$ and Corresponding Eigen Vectors are $X_{1}=\begin{bmatrix} 1\\2 \end{bmatrix}$ and $X_{2}=\begin{bmatrix} 9\\1 \end{bmatrix}$ Find the $1)\sum a_{ij},$when $i=j$ $2)Det(A)$ $3)$Sum of all Elements in the given matrix

Lakshman Bhaiya asked in Linear Algebra Oct 25, 2018

by Lakshman Bhaiya

669 views

1 vote

0 answers

95

Virtual Gate Test Series: Linear Algebra - Eigen Value

Prince Sindhiya asked in Linear Algebra Oct 16, 2018

by Prince Sindhiya

536 views

2 votes

0 answers

96

Virtual Gate Test Series: Linear Algebra - Eigen Values of a Unity Matrix

Prince Sindhiya asked in Linear Algebra Oct 15, 2018

by Prince Sindhiya

690 views

1 vote

1 answer

97

number of linearly indendent eigen vectors
... I know it can be solved using #indpendent eigen vectors = n - rank(matrix) I want to now how the above formula derived !!

MIRIYALA JEEVAN KUMA asked in Linear Algebra Oct 14, 2018

by MIRIYALA JEEVAN KUMA

1.7k views

0 votes

1 answer

98

abhishekmehta4u asked in Linear Algebra Oct 5, 2018

by abhishekmehta4u

440 views

0 votes

0 answers

99

Linear Algebra
We know, the eigen value for upper triangular/lower triangular/diagonal matrices are the diagonal elements of the matrix. https://gateoverflow.in/858/gate2002-5a This question, https://gateoverflow.in/1174/gate2005-49 If apply row transformation to convert it ... make the given matrix to upper triangular matrix, so that eigen values will be equal to the elements in the diagonals?

Swapnil Naik asked in Linear Algebra Oct 5, 2018

by Swapnil Naik

369 views

3 votes

1 answer

100

GATE2016 37 Mathematics
Let $M = \begin{bmatrix} a & b &c \\ b &d & e\\ c & e & f \end{bmatrix}$ be a real matrix with eigenvalues 1, 0 and 3. If the eigenvectors corresponding to 1 and 0 are $\left ( 1,1,1 \right )^T$ and $\left ( 1,-1, 0 \right )^T$ respectively, then the value of 3f is equal to _______.

Mk Utkarsh asked in Linear Algebra Oct 4, 2018

2.0k views

5 votes

5 answers

101

Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix

aditi19 asked in Linear Algebra Sep 20, 2018

6.9k views

1 vote

2 answers

102

ISI2016-MMA-19
Let $A$ be a real $2 \times 2$ matrix. If $5+3i$ is an eigenvalue of $A$, then $det(A)$ equals 4 equals 8 equals 16 cannot be determined from the given information

go_editor asked in Linear Algebra Sep 13, 2018

617 views

2 votes

1 answer

103

ISI2016-MMA-28
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true? $A \neq A^2$ Eigenvalues of $A^2$ are all zero rank($A$) > rank($A^2$) rank($A$) > trace($A$)

go_editor asked in Linear Algebra Sep 13, 2018

472 views

0 votes

1 answer

104

Gate 2015 CE set 2
The two eigen values of the matrix $\begin{bmatrix} 2 & 1\\ 1& p \end{bmatrix}$ have a ratio of 3:1 for p= 2. What is another value of p for which eigenvalues have the same ratio of 3:1? A)-2 b) 1 c) 7/3 d)14/3

suparna kar asked in Linear Algebra Aug 17, 2018

2.6k views

1 vote

2 answers

105

Gate 2016 CE Set 1
If the entries in each column of a square matrix M add up to 1, then an eigen value of M is A) 4 B) 3 C) 2 D) 1

suparna kar asked in Linear Algebra Aug 17, 2018

3.5k views

1 vote

1 answer

106

Inversion of a matrix - CSIR question
Let A be 3x3 matrix. Suppose 1 and -1 are two of the three Eigen Values of A and 18 is one of the Eigen Values of A2+3A. Then____ a.) Both A and A2+3A are invertible. b.) A2+3A but A is not. c.) A is invertible but A2+3A is not invertible. d.) Both A and A2+3A are not invertible.

ZeroFriction asked in Linear Algebra Jul 5, 2018

by ZeroFriction

1.3k views

1 vote

1 answer

107

linear algebra
the product of the non-zero eigen values of the matrax 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 how can we solve this question?

suneetha asked in Mathematical Logic Jul 2, 2018

324 views

3 votes

2 answers

108

Mathematics: GATE 2016 EE SET 1
Let the eigenvalues of 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 - 3A+4I would respectively, be (a) 2,14; x1,x2 (b) 2,14; x1+x2:x1-x2 (c) 2,0; x1, x2 (d) 2,0; x1+x2,x1-x2

Prateek K asked in Linear Algebra May 2, 2018

4.6k views

4 votes

1 answer

109

Made easy workbook
Let $A$ be a $4\times 4$ matrix with real entries such that $-1,1,2,-2$ are eigen values.If $B=A^4-5A^2+5I$ then trace of $A+B$ is...........

Avik Chowdhury asked in Linear Algebra Mar 22, 2018

by Avik Chowdhury

1.6k views

1 vote

1 answer

110

MadeEasy Workbook: Engineering Mathematics - Eigen value
Let $A$ be a $3\times 3$ matrix with Eigen values $-1,1,0$.Then $\mid A^{100}+I\mid$ is...

Avik Chowdhury asked in Linear Algebra Mar 22, 2018

by Avik Chowdhury

692 views

2 votes

2 answers

111

Madeeasy workbook
A $3\times 3$ matrix $P$ is such that $P^3 =P$.Then the eigenvalues of $P$ are $1,1,1$ $1,0.5+j(0.886),0.5-j(0.866)$ $1,-0.5+j(0.866),-0.5-j(0.886)$ $0,1,-1$

Avik Chowdhury asked in Linear Algebra Mar 22, 2018

by Avik Chowdhury

733 views

2 votes

2 answers

112

Madeeasy workbook
Let $A$ be a $3\times 3$ matrix such that $\mid A-I \mid=0$.If trace of $A=13$ and $det A = 32$ then sum of squares of the eigen values of $A$ is ..... $82$ $13$ $169$ $81$

Avik Chowdhury asked in Linear Algebra Mar 22, 2018

by Avik Chowdhury

8.6k views

1 vote

1 answer

113

Eigen value of the following matrix
The eigen value of the following matrix is $\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$ $1, 1, 1$ $1, 0, 0$ $3, 0, 0$ $0, 0, 0$

Prince Sindhiya asked in Linear Algebra Mar 2, 2018

by Prince Sindhiya

808 views

2 votes

1 answer

114

unitary matrix
A is a unitary matrix. Then eigen value of A are (a) 1, – 1 (b) 1, – i (c) i, – i (d) – 1, i

Prince Sindhiya asked in Linear Algebra Mar 2, 2018

by Prince Sindhiya

15.3k views

77 votes

7 answers

115

GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true

gatecse asked in Linear Algebra Feb 14, 2018

27.2k views

23 votes

6 answers

116

GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____

gatecse asked in Linear Algebra Feb 14, 2018

10.1k views

0 votes

0 answers

117

srestha asked in Linear Algebra Jan 31, 2018

696 views

4 votes

1 answer

118

largest eigen value
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)

Lakshman Bhaiya asked in Linear Algebra Jan 13, 2018

by Lakshman Bhaiya

428 views

2 votes

1 answer

119

Linear Algebra: Matrix operations
Consider two statements:- 1) Eigenvalue of M = Eigenvalue of M' {M' is the matrix gets after row operation} 2) Eigenvalue of |M- $\lambda$I| = Eigenvalue of |M- $\lambda$I|' {|M- $\lambda$I|' is the matrix gets after row operation}

Shubhanshu asked in Linear Algebra Jan 1, 2018

428 views

1 vote

0 answers

120

ankitgupta.1729 asked in Linear Algebra Dec 12, 2017

by ankitgupta.1729

749 views

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Recent questions tagged eigen-value