Intereting Posts

How do I divide a function into even and odd sections?
bound on the cardinality of the continuum? I hope not
For a fixed complex number $z$, if $z_{n}=\left( 1+\frac{z}{n}\right)^{n}$. Find $\lim_{n \to \infty}|z_{n}|$
Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
Domino Probability Problem
Complex Integration poles real axis
$f(0)=0$ and $\lvert\,f^\prime (x)\rvert\leq K\lvert\,f(x)\rvert,$ imply that $f\equiv 0$.
Can anyone extend my findings for Langford Pairings?
How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$
Bag of tricks in Advanced Calculus/ Real Analysis/Complex Analysis
Proof that operator is compact
How do we find specific values of sin and cos given the series definition
How do Taylor polynomials work to approximate functions?
Using tan(x), show that open interval is diffeomorphic with the real line
How to solve for a variable that is only in exponents?

They ask me to find all invertible matrices $A$ of the form: $\begin{bmatrix}a & b\\ c&d \end{bmatrix}$ and satisfying $A=A^{-1}$ and $A^t=A^{-1}$. I find that rather complex; does it have anything to do with orthogonality? Not sure. Any help please??

- Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
- What REALLY is the modern definition of Euclidean Spaces?
- If $A \in K^{n\times n}$ is $\{I_n , A, A^{2}, A^{3}, \dots, A^{n^{2}-1} \}$ linearly independent?
- What does $b_i\mid b_{i+1}$ mean in this context?
- Properties of special rectangle (measure)
- What is $\mathbb Z]$? What are the double brackets?
- Question about a Proof of Triangularizing a Matrix
- Consider the set of all $n\times n$ matrices, how many of them are invertible modulo $p$.
- Matrices with real entries such that $(I -(AB-BA))^{n}=0$
- Heronian triangle Generator

Hint: Given a 2×2 matrix, do you know how to compute its inverse? If not then figure out how to do that. Now that you do, take an arbitrary invertible 2×2 matrix (that is call its entries $a,b,c,d$), compute its inverse and solve the equations $A=A^{-1}$ and $A^t=A^{-1}$.

Matrices of real entries such that $AA^t=I$ are called unitary matrices and the columns of such matrices must be orthogonal.

and you want to find unitary matrices such that $A^t=A$ which are called symmetric matrices, so the answer will be all symmetric unitary matrices.

- Hardy Space Cancellation Condition
- Calculate $\sum \limits_{i=0}^n i^2 \cdot 2^i$
- The relationship between eigenvalues of matrices $XY$ and $YX$
- Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
- Alternating sum of multiple zetas equals always 1?
- Is the sum of factorials of first $n$ natural numbers ever a perfect cube?
- Is $i = \sqrt{e^{\pi\sqrt{e^{\pi\sqrt\ldots}}}}$?
- On irrationality of natural logarithm
- Proving that a sequence is Cauchy (sequence including factorials).
- Prerequisites to study cohomology?
- Prove that a set of connectives is inadequate
- What is the best way to tell people what Analysis is about?
- Covering of a CW-complex is a CW-complex
- Is it true that $0.999999999\dots=1$?
- In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.