query: How to find $A^{100}$ where $A$ is a matrix with trigonometric entries?
positive_passages.docid: 87260
positive_passages.text: Let $\theta=\frac{2 \pi}{67}$ consider the rotation matrix $A$. What is $A^{2010}$?
negative_passages.docid: 129583
negative_passages.text: Find 3x3 real matrix A such that $A^2 \neq I$ and $A^4 = I$, where I is identity matrix.
negative_passages.docid: 109736
negative_passages.text: For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$
negative_passages.docid: 3330
negative_passages.text: Square matrices, ABA = A?
negative_passages.docid: 7376
negative_passages.text: Find $\det(A^{2}+A^{T})$ when eigenvalues are $1,2,3$
negative_passages.docid: 95103
negative_passages.text: A rational matrix such that $A^{2017}=I_n$
negative_passages.docid: 150714
negative_passages.text: Quick question: matrix with norm equal to spectral radius
negative_passages.docid: 110086
negative_passages.text: Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
negative_passages.docid: 58021
negative_passages.text: Finding matrix $B$ is not zero matrix where $AB= 0$
negative_passages.docid: 129647
negative_passages.text: $A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
negative_passages.docid: 123808
negative_passages.text: How would I solve the following problem involving elementary matrices?
negative_passages.docid: 152831
negative_passages.text: When does a complex matrix have a square root?
negative_passages.docid: 129564
negative_passages.text: Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
negative_passages.docid: 16419
negative_passages.text: Is there any fast method of matrix exponentiation?
negative_passages.docid: 3150
negative_passages.text: Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
negative_passages.docid: 40973
negative_passages.text: How to find $\lfloor 1/\sqrt{1}+1/\sqrt{2}+\dots+1/\sqrt{100}\rfloor $ without a calculator?
negative_passages.docid: 45532
negative_passages.text: Let $A$ be a $n\times n$ matrix with entries $a_{ij}=i+j $ . Calculate rank of $A$