If $x$ is a $n \times 1$ vector, are the entries of diag($xx^T$) given by $x^Tx$?
2026-03-27 19:10:17.1774638617
Are the entries of diag($xx^T$) given by $x^Tx$?
352 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in VECTORS
- Proof that $\left(\vec a \times \vec b \right) \times \vec a = 0$ using index notation.
- Constrain coordinates of a point into a circle
- Why is the derivative of a vector in polar form the cross product?
- Why does AB+BC=AC when adding vectors?
- Prove if the following vectors are orthonormal set
- Stokes theorem integral, normal vector confusion
- Finding a unit vector that gives the maximum directional derivative of a vector field
- Given two non-diagonal points of a square, find the other 2 in closed form
- $dr$ in polar co-ordinates
- How to find reflection of $(a,b)$ along $y=x, y = -x$
Related Questions in QUADRATIC-FORMS
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- Questions on positivity of quadratic form with orthogonal constraints
- How does positive (semi)definiteness help with showing convexity of quadratic forms?
- Equivalence of integral primitive indefinite binary quadratic forms
- Signs of eigenvalues of $3$ by $3$ matrix
- Homogeneous quadratic in $n$ variables has nonzero singular point iff associated symmetric matrix has zero determinant.
- Trace form and totally real number fields
- Let $f(x) = x^\top Q \, x$, where $Q \in \mathbb R^{n×n}$ is NOT symmetric. Show that the Hessian is $H_f (x) = Q + Q^\top$
- Graph of curve defined by $3x^2+3y^2-2xy-2=0$
- Question on quadratic forms of dimension 3
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?
$x^Tx$ is a $1\times1$ matrix. It can't contain the $n$ diagonal values you seek. Instead, their sum is $(x^Tx)_{11}$. Using Einstein notation,$$(x^Tx)_{11}=x_ix^i=\operatorname{diag}(xx^T)_i^i=\operatorname{Trace}(xx^T),$$because $\operatorname{diag}(xx^T)_i^j=x_ix^j$.