trace

The sum of the eigenvalues of the matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2$ is ______ (rounded off to the nearest integer).

Consider a non-singular $2 \times 2$ square matrix $\mathbf{A}$. If $trace(\mathbf{A})=4$ and $trace(\mathbf{A}^2)=5$, the determinant of the matrix $\mathbf{A}$ is ________ (up to...

Consider $$3 \times 3$$ matrix with every element being equal to $$1.$$ Its only non-zero eigenvalue is __________.

If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant of the matrix is ____________.

A matrix has eigen values $$-1$$ and $$-2.$$ The corresponding eigenvectors are $$\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]$$ and $$\left[ {\matrix{ 1 \cr { - 2} \cr } } \right...

The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are

$$A = \left[ {\matrix{ 2 & 0 & 0 & { - 1} \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 3 & 0 \cr { - 1} & 0 & 0 & 4 \cr } } \right].$$ The sum of the eigen values of the matrix $$A$$ is