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  • Determinants

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  • Particular types of matrices
  • Definition of trace of a matrix
  • Cofactors
  • Determinants and operations on matrices
  • Determinants axiomatically
  • The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.
  • The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.
  • Definition of adjugate/classical adjoint of a matrix
  • A matrix is called ill-conditioned if it is nearly singular
  • The condition number of matrix measures how close it is to being singular

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  • Definition of cofactor/submatrix of a matrix
  • Definition of determinant of a matrix as a cofactor expansion across the first row
  • The determinant of a matrix can be computed as a cofactor expansion across any row.
  • The determinant of a matrix can be computed as a cofactor expansion down any column.
  • The inverse of a matrix can be expressed in terms of its matrix of cofactors.
  • Cramer's rule
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Description:Added cofactors
# Cofactors

Put content here**Cofactors:** The **cofactor** $C_{ij}$ of entry $a_{ij}$ is $C_{ij} = (-1)^{i+j} M_{ij}$, where $M_{ij}$ is the **minor** (determinant of the submatrix obtained by deleting row $i$ and column $j$). The determinant can be computed by cofactor expansion along any row or column: $\det(A) = \sum_j a_{ij}C_{ij}$.

# Parents

* Determinants
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