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Matrices

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Basic terminology and notation
Operations on matrices
Particular types of matrices
Matrix equivalence
Canonical forms of matrices
Factorization of matrices
Similarity of matrices
Nonsingular matrices and equivalences
Eigenvalues and eigenvectors
Determinants
Choosing factorizations and understanding numerical error
Rank and nullity

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Definition of column rank of a matrix
Definition of rank of a matrix
Definition of nullity of a matrix
The rank of a matrix equals number of pivots in a reduced row echelon form.
The rank of a matrix equals the rank of the linear transformation it represents.
The row space and the column space of a matrix have the same dimension.
Rank–nullity theorem for an m-by-n matrix

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Rank and nullity

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Rank–nullity theorem for an m-by-n matrixClose match
Definition of nullity of a matrixClose match
Rank and nullityClose match
Definition of rank of a matrixClose match
Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.Close match
The null space of a matrix is a subspace of R^n (or C^n).Close match
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Equivalence theorem for nonsingular matrices: the matrix A has rank n.Close match
Two matrices of the same size are equivalent if and only if they have the same rank.Close match
The rank of a matrix equals the rank of the linear transformation it represents.Close match
Subspaces associated to a matrixClose match
The rank of a matrix equals number of pivots in a reduced row echelon form.Close match
Equivalence theorem for nonsingular matrices: the dimension of the column space of A is n.Close match
Definition of nullity of a linear transformationClose match
Theorem describing the dimension of spaces associated to the block matrices of the extended reduced row echelon form of a matrixClose match
A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.Close match
The row space and the column space of a matrix have the same dimension.Close match
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The rank plus the nullity of a linear transformation equals the dimension of the domain.Close match

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