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Algebraic properties of R^n (or C^n)
Definition and terminology
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Definition of scalar
Definition of vector
Definition of column vector
Definition of R^n (or C^n)
Definition of size of a vector
Definition of entry/component of a vector
Definition of 0 vector
Definition of equality of vectors
Definition of vector sum/addition
Vector sum/addition is commutative and associative
Definition of conjugate of a vector in C^n
Definition of the real part of a vector in C^n
Definition of the imaginary part of a vector in C^n
The conjugate of a sum of vectors in C^n is the sum of the conjugates
Definition of vector-scalar multiplication
The conjugate of vector-scalar multiplication in C^n is the product of the conjugates.
Example of vector-scalar multiplication in R^2
Axioms of a vector space
Definition of vector addition
The additive inverse of a vector is called the negative of the vector.
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Algebraic properties of R^n (or C^n)
Definition and terminology
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Definition of scalar
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