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These (and other similar examples) serve as a motivation for many of the things that we do. Fibonacci sequence. The Fibonacci sequence is the sequence of numbers 1;1;2;3;5;8;13;:::, where each number is the sum of the previous two. We can use linear algebra. Linear Algebra Igor Yanovsky, 2005 4. 1 Basic Theory. 1.1 Linear Maps. If A 2 Matmxn(F) and B 2 Matnxm(F), then tr(AB) = tr(BA): Proof. Note that the (i;i) entry in AB is Pn. P j=1 fiijflji, while (j;j) entry in BA is. M i=1 fljifiij.
Vectors: Vectors and spacesLinear combinations and spans: Vectors and spacesLinear dependence and independence: Vectors and spaces
Subspaces and the basis for a subspace: Vectors and spacesVector dot and cross products: Vectors and spacesMatrices for solving systems by elimination: Vectors and spacesNull space and column space: Vectors and spaces
Functions and linear transformations: Matrix transformationsLinear transformation examples: Matrix transformationsTransformations and matrix multiplication: Matrix transformations
Linear Algebra Pdf Mit Tutorial
Inverse functions and transformations: Matrix transformationsFinding inverses and determinants: Matrix transformationsMore determinant depth: Matrix transformationsTranspose of a matrix: Matrix transformations
Orthogonal complements: Alternate coordinate systems (bases)Orthogonal projections: Alternate coordinate systems (bases)Change of basis: Alternate coordinate systems (bases)
Mit Linear Algebra Lecture Notes
Orthonormal bases and the Gram-Schmidt process: Alternate coordinate systems (bases)Eigen-everything: Alternate coordinate systems (bases)