# Exam_Sheet - u v ∈ R m • The inverse matrix and the...

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U. Washington AMATH 352 - Winter 2010 The midterm is Friday February 5th, 2010 in class. It will be closed book, no notes, no calcu- lators. You should know the deﬁnitions and the results covered in class and how to use them, including: A norm. A linear function. Linear combinations. A real linear space. The vector space R n and the space of matrices R m × n . The function spaces C 0 , C 1 , P k . A subspace (in particular, that it must be closed under addition and scalar multiplication, and hence under linear combinations). Matrix-vector and matrix-matrix multiplication, as well as addition and scalar multiplication of vectors and matrices. Linear independence. A basis for a linear space, the dimension. The null space N ( A ) and range or column space R ( A ) of a matrix. Matrix and vector transpose, A T . The Euclidian inner product of vectors
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Unformatted text preview: u , v ∈ R m . • The inverse matrix and the identity matrix. • If V is a subspace of R n then dim( V ) ≤ n . • If A ∈ R m × n then rank( A ) ≤ min( m,n ) and dim( N ( A )) = n-rank( A ) . Matlab: You should understand the following: • Deﬁning row vs. column vectors, transpose of vectors or matrices. • Colon notation for subarrays of a matrix, e.g. A(:,j) is the j th column and A(2:4,:) is a 3 × n matrix consisting of rows 2,3,4 of A ∈ R m × n . • The diﬀerence between * and .* for vector or matrix multiplication. • How to read a simple Matlab program involving for loops and interpret the results of a program. • I will not ask you to write a Matlab program, but you should be able to read a simple one. 1...
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