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3 cards from this section. Quick, good the night before a test.
Define a dual space in your own words.
Think about how vectors can be represented through functions.
What is a linear functional?
Consider the properties of functions related to vectors.
What is a dual space?
Think about mappings that preserve addition and multiplication.
True or False: The dual space of a finite-dimensional vector space has a dimension that is less than that of the original space.
Reflect on the definition of dimension in vector spaces.
Consider a finite-dimensional vector space V with basis {v_1, v_2, v_3}. Derive the form of a linear functional f: V -> R.
Focus on the linear combination of the basis vectors.
Explore how a dual space can model a complex stress state in a three-dimensional structure.
Consider each dimension in terms of physical interpretations and functional mappings.
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