Recent questions tagged eigen-value

can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.

Let A be the matrix [3112][3112]. What is the maximum value of xT Ax where the maximum is taken over all x that are the unit eigenvectors of A?A)3B)(5 + √5)/2C)3D)(...

To find out the Eigen values we put the |A-⋋I | =0 why we put the determinant =0 .Is there any specific reason For this

Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______

Suppose that the eigenvalues of matrix $A$ are $1, 2, 4$. The determinant of $\left(A^{-1}\right)^{T}$ is _________.

What is R in this question? How to solve this?Q).Let $A$ be a real $n*n$ matrix ,then which of the following statements are true?I). $A$ is orthogonal iff the row vectors...

Answer should be A. But they gave D. Their Explanation: Corresponding to each distinct eigen value, we have atleast one independent eigen vector.

For the Matrix $\begin{bmatrix} 5 & 3\\ 1& 3 \end{bmatrix}$One of the Normalised Eigen Vector is given as__________Answer $\begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-1...

The number of linearly independent Eigen vectors of is a) 0b) 1 C) 2d) infinite

Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne...

In A = (aij)nxn where aij = 1 ∀ i,j then number of different independent Eigen Vectors of A are _________ . (a) 1(b) n-1(c) 2(d) n

Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is1) $18.3...

Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ hasAn eigenvalue which is purely imaginaryAt least one real eigenvalueAt least two eigenvalues which are not ...

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 eigenvalueAny matrix $A \i...