Question:
The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is
The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is
Updated On: Mar 21, 2024
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The correct answer is(A): 0
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Top Questions on Eigenvectors
- Consider the line integral \( \int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r} \), where \( \mathbf{F}(\mathbf{r}) = x \hat{\mathbf{i}} + y \hat{\mathbf{j}} + z \hat{\mathbf{k}} \), with \( \hat{\mathbf{i}}, \hat{\mathbf{j}}, \) and \( \hat{\mathbf{k}} \) as unit vectors in the (x, y, z) Cartesian coordinate system. The path \( C \) is given by \( \mathbf{r}(t) = \cos(t) \hat{\mathbf{i}} + \sin(t) \hat{\mathbf{j}} + t \hat{\mathbf{k}} \), where \( 0 \leq t \leq \pi \). The value of the integral, rounded off to 2 decimal places, is _____
- The eigenvectors of the matrix are:
\(A=\left(\begin{matrix} i & 1 \\ 2 & -i \end{matrix}\right)\)
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