If I have a squared symmetric matrix $X(m,m)$ which is a result of the product: $X =Y^T A Y$, in which $Y(n,m)$; and $A(n,n)$ is a diagonal matrix.
My question is: Is it possible to get the original $Y$ and $A$ matrices from $X$?
2026-03-25 04:36:25.1774413385
Matrix decomposition to its original product
41 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 SYMMETRIC-MATRICES
- $A^2$ is a positive definite matrix.
- Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$
- Is $A-B$ never normal?
- Is a complex symmetric square matrix with zero diagonal diagonalizable?
- Symmetry of the tetrahedron as a subgroup of the cube
- Rotating a matrix to become symmetric
- Diagonalize real symmetric matrix
- How to solve for $L$ in $X = LL^T$?
- Showing a block matrix is SPD
- Proving symmetric matrix has positive eigenvalues
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?