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Questions and Answers
What can be said about the set L(A) of all linear combinations of elements of a set A?
What can be said about the set L(A) of all linear combinations of elements of a set A?
Why does L(A) include each ai?
Why does L(A) include each ai?
What can be said about a subspace W that includes A?
What can be said about a subspace W that includes A?
How can a sum of two linear combinations of elements of A be rewritten?
How can a sum of two linear combinations of elements of A be rewritten?
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What does it mean for a set A to span a vector space V?
What does it mean for a set A to span a vector space V?
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Is the function space on an infinite set A always finite-dimensional?
Is the function space on an infinite set A always finite-dimensional?
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What is the space of all mappings f: A -> W?
What is the space of all mappings f: A -> W?
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What is Hom(V, W)?
What is Hom(V, W)?
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What is the theorem 3.2 stating?
What is the theorem 3.2 stating?
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Why is Hom(V, W) a subspace?
Why is Hom(V, W) a subspace?
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What is the theorem 3.3 stating?
What is the theorem 3.3 stating?
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What is the result of the composition of linear maps?
What is the result of the composition of linear maps?
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What is the value of L~ at t, given the coefficients xi and functions Ii?
What is the value of L~ at t, given the coefficients xi and functions Ii?
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What is the image of ~1 under the linear mapping T?
What is the image of ~1 under the linear mapping T?
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What is the set of all real-valued functions on IR?
What is the set of all real-valued functions on IR?
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What is the theorem that states that every linear mapping from IRn to W is of a certain form?
What is the theorem that states that every linear mapping from IRn to W is of a certain form?
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What is the coefficient of et in the linear combination L~?
What is the coefficient of et in the linear combination L~?
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What is the spanning set for IRn?
What is the spanning set for IRn?
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What is the property of the linear combination map T?
What is the property of the linear combination map T?
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What is the result of T(x + y) in terms of T(x) and T(y)?
What is the result of T(x + y) in terms of T(x) and T(y)?
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What is the significance of the theorem in this context?
What is the significance of the theorem in this context?
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What is the notation La for?
What is the notation La for?
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What is the skeleton of a linear mapping T?
What is the skeleton of a linear mapping T?
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What is the relationship between the map a -> La and the set of all linear maps T from IR to W?
What is the relationship between the map a -> La and the set of all linear maps T from IR to W?
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What is the topic of Chapter 3 in the table of contents?
What is the topic of Chapter 3 in the table of contents?
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What is the title of the chapter that deals with 'Bases Dimension The dual space'?
What is the title of the chapter that deals with 'Bases Dimension The dual space'?
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What comes after 'Chapter 3' in the table of contents?
What comes after 'Chapter 3' in the table of contents?
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What is the topic of the chapter marked with a *?
What is the topic of the chapter marked with a *?
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How many chapters are there in the table of contents?
How many chapters are there in the table of contents?
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