'Linear vector space' diaporamas de présentation

D. R. Wilton ECE Dept.

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Math Foundations of CG

Math Foundations of CG. Outline. Abstract spaces: objects and operations Field of real numbers R Vector space over R Euclidean spaces Affine spaces Affine combinations Convex combinations Frames Affine maps Euclidean spaces Read: angel, Appendices B and C, Ch 4.1-4.3. Geometric ADTs.

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Arkadij Zakrevskij United Institute of Informatics Problems of NAS of Belarus

A NEW ALGORITHM TO SOLVE OVERDEFINED SYSTEMS OF LINEAR LOGICAL EQUATIONS. Arkadij Zakrevskij United Institute of Informatics Problems of NAS of Belarus. Outline. How the problem is stated How the problem can be solved Theoretical background Example Solving the core equation Experiments

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App III. Group Algebra & Reduction of Regular Representations

App III. Group Algebra & Reduction of Regular Representations. Group Algebra Left Ideals, Projection Operators Idempotents Complete Reduction of the Regular Representation. III.1. Group Algebra. Definition III.1: Group Algebra

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II. Linear Geometry of n -Space

II. Linear Geometry of n -Space. Vectors in Space Length and Angle Measures. II.1. Vectors in Space. See Apostol, Chap 1. Descartes: Points in plane ~ ( a 1 , a 2 ), points in space ~ ( a 1 , a 2 , a 3 ).

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Tensors

Tensors. Transformation Rule. A Cartesian vector can be defined by its transformation rule. Another transformation matrix T transforms similarly. x 3. x 2. x 1. For a Cartesian coordinate system a tensor is defined by its transformation rule.

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Vectors

Vectors. Two Operations. Many familiar sets have two operations. Sets: Z , R , 2 ? 2 real matrices M 2 ( R ) Addition and multiplication All are groups under addition. 0 is a problem for multiplication. Without 0 the sets are groups Multiplication is not commutative for M 2 ( R ).

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Appendix II: Summary Of Linear Vector Spaces

Appendix II: Summary Of Linear Vector Spaces. II.1. Linear Vector Space II.2. Linear Transformations (Operators) on Vector Spaces II.3. Matrix Representation of Linear Operators II.4. Dual Space, Adjoint Operators II.5. Inner (Scalar) Product and Inner Product Space

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