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10_21_terms_to_know

# 10_21_terms_to_know - Cofactors Concept Questions 1 Explain...

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Prelim Prep: Concepts (3.6-5.2, 8.2) MA2940: Linear Algebra for Engineers Terms to be Familiar With: Space, Subspace, Lin. Transformation (know defs) Fundamental Subspaces: RS,CS,NS,LNS Fundamental Theorem of Linear Algebra (funny pic- ture?) Orthogonal Subspaces Orthogonal Complements Projection (onto vector, onto subspace) Projection matrix Positive deﬁnite/ semideﬁnite Least Squares Approximation Normal equations Orthogonal vectors Orthonormal vectors Orthnormal matrix Orthogonal matrix Gram-Schmidt process QR factorization Directed Graph Incidence Matrix Kirchkoﬀ’s Laws Ohm’s Law Determinants “Big Formula” for determinants
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Unformatted text preview: Cofactors Concept Questions 1. Explain the diﬀerence between orthogonal matrices and orthonormal matrices. 2. Explain the diﬀerence between orthogonal and orthonormal vectors. 3. How many basis vectors are needed to describe the subspace of R 4 deﬁned by x-y = 0? 4. ( T / F ) If the columns of a matrix A are linearly independent, then so will be the columns after applying the Gram-Schmidt process. 5. ( T / F ) If A is orthonormal, A ( A T A )-1 A T = AA T . 6. ( T / F ) If the columns of A are orthonormal, then the rows of A are orthogonal. 1 TA: Kyle Wilson...
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