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- Ch. 5 Determinants Determinant functions
- 1 Introduction Section 3: Topology of 2-orbifolds
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- 7.4. Computations of Invariant Let A be nxn matrix with entries in F[x].
- 8_6 Singular value decomposition Diagonalizations
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- Chapter 2: Vector spaces Vector spaces, subspaces, basis,
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- Matrix notation, operations, row and column vectors, product AB(important), transpose
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- 7.2. Cyclic decomposition and rational forms
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- Deformation spaces of real projective structures on Coxeter 3-orbifolds
- A survey of structures on
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- 1 Introduction About this lecture
- 6. Elementary Canonical How to characterize a
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- 7.3. Jordan form Canonical form for matrices and
- 1 Introduction About this lecture
- 6.3. Annihilating polynomials Cayley-Hamilton theorem
- 8.4. Quadratic Forms Quadratic forms generalize norm, lengths, inner-products,..
- Rank+nullity=dimension The dimension theorem for
- A method to find A-1 Elementary operations
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- Geometric structures on 2-orbifolds
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- 1 Introduction About this lecture
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- LU decomposition L: lower triangular
- 1 Introduction About this lecture
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- 7_5. The rank theorem Column rank = row rank.
- Logic and the set theory Lecture 1: Introduction
- Chapter 4 Determinants Determinants are useful because it gives us
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- 1 Introduction About this lecture
- 1 Introduction About this lecture
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- 8.5. Applica+on of Quadra+c forms to op+miza+on
- In many cases, such as finding eigenvalues, it is difficult to obtain an exact values.
- 4.3. Cramer's Rules and applications of determinant C_ij cofactor of A_ij
- 1 Introduction About this lecture
- 7_5. The rank theorem Column rank = row rank.
- A composition of functions: f:X->Y,g:Y->Z, we obtain gf:X->Z.
- This should be at least 10 pages long with 12 pt font and double spaced. Due by Monday 4:00 pm February 16th 2009.
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- 1 Introduction About this lecture
- Kernel of a linear transformation
- 7.6 The pivot theorem Basis problem
- 1 Introduction About this lecture
- 6.6 Direct sum decompositions
- 3.6. Double dual Dual of a dual space
- 7.6 The pivot theorem Basis problem
- Section 1: Rational Forms 7.1. Rational forms
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- 7.8 Best approxima0on and least We wish to find the best
- 7.7. The projection theorem and its
- 5.4. Additional properties Cofactor, Adjoint matrix,
- A subspace is a set one can do scalar multiplication and addition and not leave the
- Rank+nullity=dimension The dimension theorem for
- Solutions for inhomogeneous systems. Consistency
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- diagonalizability Symmetric matrices can be diagonalized by an
- 1 Introduction About this lecture
- Matrix of a linear operator with respect to a One can use different representation of a
- Diagonal matrix, triangular matrix, symmetric and skew-symmetric matrices,AAT, Fixed points, inverting
- 7.2. Cyclic decomposition and rational forms
- Polynomial Ideals Euclidean algorithm
- A method to find A-1 Elementary operations
- Ax=x. (I-A)x=0. If I-A is invertible, then there are only trivial
- For 2x2 matrix det(A)=det(AT). In general we have
- 1 Introduction About this lecture
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- Geometric structures on 2-orbifolds Section 1: Manifolds and differentiable structures
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- 1 Introduction About this lecture
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- For 2x2 matrix det(A)=det(AT). In general we have
- 7_3 The fundamental spaces of a matrix.
- diagonalizability Symmetric matrices can be diagonalized by an
- LU decomposition L: lower triangular
- 6.4 Composition and invertibility of linear transformations
- Bases for subspaces Consider V=Span{v_1,v_2,...,v_l}.
- Logic and the set theory Lecture 7, 8: Predicate Logic
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- Logic and the set theory Lecture 19: The set theory
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- Logic and the set theory Lecture 14: Proofs in How to Prove It.
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- Logic and the set theory Lecture 21: The set theory: Review Sections 12-25
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