If Q is the change of coordinates matrix From some basis B to B', then Q inverse is the change of coordinates matrix from B' to B? Is this true?
I think/ know it is the, but don't know how to prove it
2026-04-02 22:07:07.1775167627
Change of Coordinates matrix.
95 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in COORDINATE-SYSTEMS
- How to change a rectangle's area based on it's 4 coordinates?
- How to find 2 points in line?
- Am I right or wrong in this absolute value?
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- inhomogeneous coordinates to homogeneous coordinates
- Find the distance of the point $(7,1)$ from the line $3x+4y=4$ measured parallel to the line $3x-5y+2=0.$
- A Problem Based on Ellipse
- Convert a vector in Lambert Conformal Conical Projection to Cartesian
- Archimedean spiral in cartesian coordinates
- How to find the area of the square $|ABCD|$?
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?
It's true, and it is a consequence of linearity and the definion of inverse matrix. If you have a Basis $\{\mathbf{e}_i\}$ and a linear transformation $\mathbf{e'}_i=Q\mathbf{e}_i$ than : $\mathbf{e}_i=I\mathbf{e}_i=Q^{-1}Q\mathbf{e}_i=Q^{-1}\mathbf{e'}_i$, and since any vector $\mathbf{v}$ can be expressed as a linear combination $\mathbf{v}=\sum_i v_i\mathbf{e}_i$, the same hold for any vector.