Vector Space (Review) by Rashad Wattu

Mathematical vector space is a crucial and fundamental idea. It depends on the concept of field. These notes were primarily written to help maths students understand vector space, which is a concept that they all need to be familiar with.

We are very thankful to Rashad Wattu for providing these notes and appreciates his effort to publish these notes on MathCity.org

• Definition: Vector Space
• Examples
• Subspace, examples, trivial subspace, non-trivial subspace
• Union of subspaces
• Intersection of subspaces
• Sum of subspaces
• Direct sum
• Linear combination and spanning sets
• Spanning sets
• Null spaces
• Column spaces
• Linear transformation
• Linearly independent sets
• Linearly dependent sets
• Basis and dimension
• Finite dimension vector space.
• Finite and infinite dimension vector space.
• Spanning set theorem
• Rank theorem
• Invertible matrix theorem
• Eigen values and eigen vectors
• Eigen space
• Orthogonal matrix

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