Integral Calc: Linear Algebra

The Series Includes : Integral Calc: Adding and scaling linear transformations | Angle between vectors | Basis | Cauchy-Schwarz inequality | Compositions of linear transformations | Coordinates in a new basis | Cramer's rule for solving systems | Cross products | Determinants | Dimensionality, nullity, and rank | Dot and cross products as opposite ideas | Dot products | Eigen in three dimensions | Eigenvalues, eigenvectors, eigenspaces | Equation of a plane, and normal vectors | Functions and transformations | Gauss-Jordan elimination | Gram-Schmidt process for change of basis | Identity matrices | Inverse of a transformation | Inverse transformations are linear | Invertibility from the matrix-vector product | Least squares solution | Linear combinations and span | Linear independence in three dimensions | Linear independence in two dimensions | Linear subspaces | Linear systems in three unknowns | Linear systems in two unknowns | Linear transformations as matrix-vector products | Linear transformations as rotations | Matrix addition and subtraction | Matrix dimensions and entries | Matrix inverses, and invertible and singular matrices | Matrix multiplication | Modifying determinants | Multiplying matrices by vectors | Null and column spaces of the transpose | Null space of a matrix | Number of solutions to the linear system | Orthogonal complements | Orthogonal complements of the fundamental subspaces | Orthonormal bases | Pivot entries and row-echelon forms | Preimage, image, and the kernel | Projection onto an orthonormal basis | Projection onto the subspace | Projections as linear transformations | Representing systems with matrices | Scalar multiplication | Simple row operations | Solving Ax=b | Solving systems with inverse matrices | Spans as subspaces | The column space and Ax=b | The elimination matrix | The null space and Ax=O | The product of a matrix and its transpose | Transformation matrices and the image of the subset | Transformation matrix for a basis | Transposes and their determinants | Transposes of products, sums, and inverses | Unit vectors and basis vectors | Upper and lower triangular matrices | Using determinants to find area | Vector operations | Vector triangle inequality | Vectors | Zero matrices

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Description

This series includes everything from Linear Algebra, including operations on one matrix, including solving linear systems, and Gauss-Jordan elimination, operations on two matrices, including matrix multiplication and elimination matrices, matrices as vectors, including linear combinations and span, linear independence, and subspaces, dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities, matrix-vector products, including the null and column spaces, and solving Ax=b, transformations, including linear transformations, projections, and composition of transformations, inverses, including invertible and singular matrices, and solving systems with inverse matrices, determinants, including upper and lower triangular matrices, and Cramer's rule, transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose, orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis, orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process, eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions.

Length: 878 minutes

Item#: BVL275835

Copyright date: ©2019