Find a 2 × 2 matrix that rotates a plane by +45° (+45° means 45° counterclockwise).
2026-04-03 09:35:34.1775208934
how to get the result of matrices
57 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in MATRIX-EQUATIONS
- tensor differential equation
- Can it be proved that non-symmetric matrix $A$ will always have real eigen values?.
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- How to differentiate sum of matrix multiplication?
- Do all 2-variable polynomials split into linear factors over the space of $2 \times 2$ complex matrices?
- Big picture discussion for iterative linear solvers?
- Matrix transformations, Eigenvectors and Eigenvalues
- Jordan chevaley decomposition and cyclic vectors
- If $A$ is a $5×4$ matrix and $B$ is a $4×5$ matrix
- Simplify $x^TA(AA^T+I)^{-1}A^Tx$
Related Questions in MATRIX-DECOMPOSITION
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- Swapping row $n$ with row $m$ by using permutation matrix
- Block diagonalizing a Hermitian matrix
- $A \in M_n$ is reducible if and only if there is a permutation $i_1, ... , i_n$ of $1,... , n$
- Simplify $x^TA(AA^T+I)^{-1}A^Tx$
- Diagonalize real symmetric matrix
- How to solve for $L$ in $X = LL^T$?
- Q of the QR decomposition is an upper Hessenberg matrix
- Question involving orthogonal matrix and congruent matrices $P^{t}AP=I$
- Singular values by QR decomposition
Related Questions in MATRIX-RANK
- Bases for column spaces
- relation between rank of power of a singular matrix with the algebraic multiplicity of zero
- How to determine the rank of the following general $\mathbb{R}$-linear transformation.
- How to prove the dimension identity of subspace? i.e. $\dim(V_1) + \dim(V_2) = \dim(V_1 + V_2) + \dim(V_1 \cap V_2)$
- How can I prove that $[T]_B$ is a reversible matrix?
- can I have $\det(A+B)=0$ if $\det(A)=0$ and $\det(B) \neq 0$?
- Let $A$ be a diagonalizable real matrix such as $A^3=A$. Prove that $\mbox{rank}(A) = \mbox{tr}(A^2)$
- Row permuation of a matrix for a non-zero diagonal
- Tensor rank as a first order formula
- Rank of Matrix , Intersection of 3 planes
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Hint: it is easy to find a square root of a diagonal matrix, $D$, with nonnegative entries $d_i$ on the diagonal: it is simply another diagonal matrix, $D^{1/2}$, where each entry is $\pm \sqrt{d_i}$.
A similar trick works to find $X$ so $X^2=A$ when $A$ is diagonalizable. If $A=PDP^{-1}$, then $X=PD^{1/2}P^{-1}$ is a solution.
In your case, your matrix $A$ is diagonalizable.