Prove that every symmetric matrix can be diagonalized using similarity transformation even if it has repeated eigenvalue by showing that the Jordan form of a symmetric matrix has no Jordan block of order 2.
2026-03-27 16:47:06.1774630026
Prove that every symmetric matrix can be diagonalized using similarity transformation even if it has repeated eigenvalue
166 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SYMMETRIC-GROUPS
- Orbit counting lemma hexagon
- A "Restricted Sudoku" Symmetry Group Question
- Show, by means of an example, that the group of symmetries of a subset X of a Euclidean space is, in general, smaller than Sym(x).
- Prove that $\sigma$ is a power of $\tau$ when they commute $\sigma\tau=\tau\sigma$.
- Proof verification - the only group of order 24 without normal sylow subgroup is $S_4$.
- Symmetry subgroup of a cube
- Subgroup generated by $S$ is $A_5$
- Question about semigroups of permutations
- Symmetry of the tetrahedron as a subgroup of the cube
- Interpretation of wreath products in general and on symmetric groups
Related Questions in DIAGONALIZATION
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- 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?
- Let $A$ be a diagonalizable real matrix such as $A^3=A$. Prove that $\mbox{rank}(A) = \mbox{tr}(A^2)$
Related Questions in JORDAN-NORMAL-FORM
- Simultaneous diagonalization on more than two matrices
- $ \exists \ g \in \mathcal{L}(E)$ s.t. $g^2 = f \ \iff \forall \ k$, $\dim \ker(f-aId)^k$ is even
- Relation between left and right Jordan forms
- About Matrix function on Jordan normal form
- Generalized Eigenvectors when algebraic multiplicity greater than 1
- Commutativity and Jordan Decomposition
- Jordan forms associated with characteristic polynomials and minimal polynomials
- Jordan's Canonical Form of a Matrix
- $3 \times 3$-matrices with the same characteristic polynomials and minimal polynomials that are not similar
- Jordan form of a matrix confusion
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?