Why is the word expansion used? What does it mean here?
2026-03-27 22:52:50.1774651970
Determinant of a matrix. Why is it called an expansion of cofactors?
106 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 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 DETERMINANT
- Form square matrix out of a non square matrix to calculate determinant
- Let $T:V\to W$ on finite dimensional vector spaces, is it possible to use the determinant to determine that $T$ is invertible.
- Optimization over images of column-orthogonal matrices through rotations and reflections
- Effect of adding a zero row and column on the eigenvalues of a matrix
- Geometric intuition behind determinant properties
- Help with proof or counterexample: $A^3=0 \implies I_n+A$ is invertible
- Prove that every matrix $\in\mathbb{R}^{3\times3}$ with determinant equal 6 can be written as $AB$, when $|B|=1$ and $A$ is the given matrix.
- Properties of determinant exponent
- How to determine the characteristic polynomial of the $4\times4$ real matrix of ones?
- The determinant of the sum of a positive definite matrix with a symmetric singular 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?
Frequently it happens that in a set of objects that can be composed together in some way, there are objects that are for some reason simpler than others.
In this circumstances it can be convenient to be able to find how simpler objects combine to give an object.
Once found, one can say that the object is decomposed over the simpler objects, but no insight into how simpler objects compose is given.
If the composition is a sum of the simpler objects each multiplied by a factor then one can use the espression "the object is expanded by the simpler objects". (See e.g. vector expansion, Taylor or Fourier expansion)
If the composition is a product of the simpler objects each raised to some power then one can use the espression "the object is factored into the simpler objects". (See e.g. integer factorization or polynomial factorization)
Cofactor = complement of factor
$C_{11}$ is the complement of the factor $a_{11}$. It is the complement because it is computed by complementation of $a_{11}$ w.r.t. the matrix, that is, by eliminating by the matrix the row and the column containing $a_{11}$.