Is every complex square matrix is unitarily similar to a lower triangular matrix?
I know that by Schur's Lemma, upper triangular matrices would suffice, but what about lower. Intuitively, I think it should, but I lack a proof that would back it.
2026-03-25 09:48:18.1774432098
Every complex square matrix is unitarily similar to a lower triangular matrix?
60 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in UNITARY-MATRICES
- Operator norm and unitary matrix
- Unitary matrices are invertible.
- Square root of unitary matrix
- $AA^*A=A$ with eigenvalues $1$ and $0$, prove that $A$ is unitarily diagonalizable.
- Modifying unitary matrix eigenvalues by right multiplication by orthogonal matrix
- Parametrization of unitary matrices
- Is real power of unitary matrix unitary?
- How to calculate the unitaries satisfying $U_YXU_Y^\dagger=Y$ and $U_ZXU_Z^\dagger=Z$?
- A real symmetric cannot be similar to an antisymmetric matrix
- Numerical stability: cannot unitarily diagonalize normal matrices
Related Questions in SIMILAR-MATRICES
- Does every polynomial with a Perron root have a primitive matrix representation?
- Looking for verification that I correctly showed these matrices are similar
- Matrices similar to nilpotent
- Find the values of $a$ and $b$ such that the following matrices are similar
- Sufficient condition for a matrix to be diagonalizable and similar matrices
- Diagonalizable matrices with same geometric multiplicity for every eigenvalue similar?
- Proving two matrices are similar using the characteristic polynomial
- Is every matrix conjugate to its transpose in a continuous way?
- How do I find out that the following two matrices are similar?
- Similarity of $2 \times 2$ matrices
Related Questions in SCHUR-DECOMPOSITION
- Schur factorization from spectral decomposition
- 2 by 2 Schur Decomposition
- How does MATLAB compute the real Schur decomposition?
- Finding spectrum with Schur decomposition
- How to prove the changing of basis matrices is unitary matrices
- Codable Algorithm to the generalised Complex Schur Decomposition without using Inbuilt functions
- Convergence of the complex QR algorithm to Schur decomposition
- Schur decomposition of a "flipped" triangular matrix
- Schur decomposition to show matrix has $n$ orthonormal eigenvectors
- Schur decomposition for $3 \times 3$ matrix
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?
Since the transpose of your matrix is similar to an upper triangular matrix (just as you say), transposing the similarity, you get what you want.