Recent questions tagged matrix

if $A^{3} = 0$ can we conclude that $A^{2} = A$ that will be valid for zero matrix

Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ is a real vector $[x_1,x_2]^T$ with length $||{\vec{x}}||$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of th...

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$

Consider matrix $A =$ $\begin{bmatrix} k &2k \\ k^{2}-k &k^{2} \end{bmatrix}$ and $x =$ $\begin{bmatrix} x1\\x2 \end{bmatrix}$The number of distinct real values of $k$ f...

For the matrix $A = \begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ if $\textit{det}$ stands for the determinant and $A^T$ is the transp...

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 inverseP has ...

In the LU decomposition of the matrix,$\begin{bmatrix} 1 &2 \\ 3 &8 \end{bmatrix}$ if the diagonal elements of $U$ are both $1$, then the trace of $L$ is$?$

If $A=\begin{bmatrix} cos \alpha & sin \alpha \\ -sin \alpha & cos \alpha \end{bmatrix}$be such that $A +A ^{'}=I$ then the value of $\alpha$ is

Let $M=\begin{pmatrix} 6 & 2\\ -2& -3 \end{pmatrix}$then trace of $M^{5}$

A scalar valued function is defined as $f(x)=x^TAx+b^Tx+c$ , where A is a symmetric positive definite matrix with dimension $n*1$ ; b and x are vectors of dimension $n*1...