This is from my textbook
Why the column of the new design matrix are orthogonal? for example, let say
$A=\begin{pmatrix} 1& 1& 4\\ 1& 2& 0\\ 1& 3& 2 \end{pmatrix}$
how to caclulate the mean-deviation form of matrix A?
2026-03-31 06:27:22.1774938442
mean-deviation form, why orthogonal?
919 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 VECTOR-SPACES
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Does curl vector influence the final destination of a particle?
- Closure and Subsets of Normed Vector Spaces
- Dimension of solution space of homogeneous differential equation, proof
- Linear Algebra and Vector spaces
- Is the professor wrong? Simple ODE question
- Finding subspaces with trivial intersection
- verifying V is a vector space
- Proving something is a vector space using pre-defined properties
- Subspace of vector spaces
Related Questions in PROJECTIVE-GEOMETRY
- Visualization of Projective Space
- Show that the asymptotes of an hyperbola are its tangents at infinity points
- Determining the true shape of a section.
- Do projective transforms preserve circle centres?
- why images are related by an affine transformation in following specific case?(background in computer vision required)
- Calculating the polar of a given pole relative to a conic (with NO Calculus)
- Elliptic Curve and Differential Form Determine Weierstrass Equation
- Inequivalent holomorphic atlases
- Conic in projective plane isomorphic to projective line
- Noether normalization lemma
Related Questions in LEAST-SQUARES
- Is the calculated solution, if it exists, unique?
- Statistics - regression, calculating variance
- Dealing with a large Kronecker product in Matlab
- How does the probabilistic interpretation of least squares for linear regression works?
- Optimizing a cost function - Matrix
- Given matrix $Q$ and vector $s$, find a vector $w$ that minimizes $\| Qw-s \|^2$
- Defects of Least square regression in some textbooks
- What is the essence of Least Square Regression?
- Alternative to finite differences for numerical computation of the Hessian of noisy function
- Covariance of least squares parameter?
Related Questions in MEANS
- Arithmetic and harmonic mean of two numbers.
- Mean and variance of $X:=(k-3)^2$ for $k\in\{1,\ldots,6\}$.
- Reason generalized linear model
- How do you calculate the probability of the difference between two normal distribution
- Calculating standard deviation without a data set.
- Compute the variance of $S = \sum\limits_{i = 1}^N X_i$, what did I do wrong?
- Find out if $\hat{\tau}$ is an unbiased estimator
- Computing mean and variance of custom distribution
- Prove $\lim\limits_{n \to \infty} \frac{\log (n!)}{n \sqrt[n]{\log 2 \cdot \log 3 \cdots \log n}}=1$
- How to tell when a data series is a normal distribution
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?
Without the details of how the matrix $\mathbf{A}$ was formed, we are restricted to guessing.
Suppose $\mathbf{A}$ is a collection of column vectors $$ \mathbf{A} = \left[ \begin{array}{ccc} x_{1} & x_{2} & x_{3} \end{array} \right] $$ The transformation would be $$ \tilde{x}_{k} = x_{k} - \bar{x}. $$ The transformed matrix is $$ \tilde{\mathbf{A}} = \left[ \begin{array}{crr} 0 & -1 & 2 \\ 0 & 0 & 0 \\ 0 & 1 & -2 \\ \end{array} \right] $$ Quick check: the columns all have sum $0$.