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4 cards from this section. Quick, good the night before a test.
What is an inner product?
Think about how this relates to measuring angles and lengths.
Why are orthogonal vectors important in numerical methods?
Consider how orthogonal vectors relate to projections.
What is the role of inner products in matrix assembly?
Consider the geometric interpretation of inner products.
True or False: Projections are used to maximize the error in numerical modeling.
Think about what projections aim to achieve.
Expand on the inner product approach to develop a method for minimizing errors in a numerical model used for aerospace structures. What considerations should be made regarding stability and accuracy?
Think about the physical properties of materials and how they relate to inner product concepts.
Design an experiment using Gram-Schmidt orthogonalization in a computational setting to solve a structural stability problem. Describe the steps and expected outcomes.
Consider how basis vectors will affect the resulting matrix.
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