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Definition of scalar
Definition of vector-scalar multiplication
Axioms of a vector space
Definition of vector addition
The additive inverse of a vector is called the negative of the vector.
Definition of vector

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The additive inverse of a vector is called the negative of the vector.

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The additive inverse of a vector equals the vector multiplied by -1.Close match
The additive inverse of a vector is unique.Close match
Definition of vector additionClose match
Definition of inverse of a linear transformationClose match
Definition of vector sum/additionClose match
The 0 scalar multiplied by any vector equals the 0 vector.Close match
Definition of 0 vectorClose match
The inverse of the inverse of a linear transformation is the original linear transformationClose match
The inverse of an isomorphism is an isomorphism.Related
Basic propertiesRelated
The 0 vector is unique.Related
The eigenvalues of the inverse of a nonsingular matrix are the reciprocals of the eigenvalues.Related
Vector sum/addition is commutative and associativeRelated
The inverse of a scalar multiple is the reciprocal times the inverse.Related
Definition of vectorRelated
The inverse of a linear transformation is a linear transformationRelated
Matrix inverse is an involution.Related
The adjoint of a sum is the sum of the adjoints.Related
Definition of inverse of a matrixRelated
The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.Related

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