What number $b$ in \begin{bmatrix} 3 & b \\ 1 & 0 \end{bmatrix} makes $A = Q\Lambda Q^T$ possible?
2026-03-25 01:33:31.1774402411
Solving for Unknown in Matrix
37 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 EIGENVALUES-EIGENVECTORS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Show that this matrix is positive definite
- Is $A$ satisfying ${A^2} = - I$ similar to $\left[ {\begin{smallmatrix} 0&I \\ { - I}&0 \end{smallmatrix}} \right]$?
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Question on designing a state observer for discrete time system
- Evaluating a cubic at a matrix only knowing only the eigenvalues
- Eigenvalues of $A=vv^T$
- A minimal eigenvalue inequality for Positive Definite Matrix
- Construct real matrix for given complex eigenvalues and given complex eigenvectors where algebraic multiplicity < geometric multiplicity
Related Questions in DIAGONALIZATION
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Show that $A^m=I_n$ is diagonalizable
- Simultaneous diagonalization on more than two matrices
- Diagonalization and change of basis
- Is this $3 \times 3$ matrix diagonalizable?
- Matrix $A\in \mathbb{R}^{4\times4}$ has eigenvectors $\bf{u_1,u_2,u_3,u_4}$ satisfying $\bf{Au_1=5u_1,Au_2=9u_2}$ & $\bf{Au_3=20u_3}$. Find $A\bf{w}$.
- Block diagonalizing a Hermitian matrix
- undiagonizable matrix and annhilating polynom claims
- Show that if $\lambda$ is an eigenvalue of matrix $A$ and $B$, then it is an eigenvalue of $B^{-1}AB$
- Is a complex symmetric square matrix with zero diagonal diagonalizable?
Related Questions in TRANSPOSE
- Vectorization and transpose: how are $\text{vec}(W^T)$ and $\text{vec}(W)$ related?
- What can we say about two bases A and B for which the conversion matrix to a third base C is the transpose of the other
- Decomposition of the product of matrices
- Interpretation of transpose of a linear application from a matricial product point of view
- Derivative involving trace and Kronecker product
- What does a matrix multiplied by its transpose tell me about the matrix's inverse?
- Proving similarity of $A$ and $A^T$
- What does it mean when you say a matrix of of a linear transformation is relative to a standard basis?
- Matrix equation $Z - {}^t Z =c A Z$
- Prove that the characteristic polynmial of a skew mapping satisfies $c(-\lambda) = (-1)^n c(\lambda)$
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 Notice that if $A = Q\Lambda Q^T$ then $A^T=A$.
UPDATE
I am assuming $\Lambda$ is real-valued. If you assume $\Lambda$ is diagonal, $A$ must be symmetric so $b=1$. Without any assumptions on $\Lambda$, as Laray indicated, $A$ must be normal...