Become a Linear Algebra Master by Udemy
Learn everything from Linear Algebra, then test your knowledge with 400+ practice questions
Course Highlights
- 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
Skills you will learn!
Curriculum
4 Topics
What we'll learn in this course
How to get the most out of this course
Download the formula sheet
The EVERYTHING download
27 Topics
Introduction to operations on one matrix
RESOURCE: Quiz solutions for this section
Linear systems in two unknowns
Linear systems in two unknowns
Linear systems in two unknowns
Linear systems in three unknowns
Linear systems in three unknowns
Linear systems in three unknowns
Matrix dimensions and entries
Matrix dimensions and entries
Matrix dimensions and entries
Representing systems with matrices
Representing systems with matrices
Representing systems with matrices
Simple row operations
Simple row operations
Simple row operations
Pivot entries and row-echelon forms
Pivot entries and row-echelon forms
Pivot entries and row-echelon forms
Gauss-Jordan elimination
Gauss-Jordan elimination
Gauss-Jordan elimination
Number of solutions to the linear system
Number of solutions to the linear system
Number of solutions to the linear system
BONUS! Extra practice problems. :)
21 Topics
Introduction to operations on two matrices
RESOURCE: Quiz solutions for this section
Matrix addition and subtraction
Matrix addition and subtraction
Matrix addition and subtraction
Scalar multiplication
Scalar multiplication
Scalar multiplication
Zero matrices
Zero matrices
Zero matrices
Matrix multiplication
Matrix multiplication
Matrix multiplication
Identity matrices
Identity matrices
Identity matrices
The elimination matrix
The elimination matrix
The elimination matrix
BONUS! Extra practice problems. :)
30 Topics
Introduction to matrices as vectors
RESOURCE: Quiz solutions for this section
Vectors
Vectors
Vectors
Vector operations
Vector operations
Vector operations
Unit vectors and basis vectors
Unit vectors and basis vectors
Unit vectors and basis vectors
Linear combinations and span
Linear combinations and span
Linear combinations and span
Linear independence in two dimensions
Linear independence in two dimensions
Linear independence in two dimensions
Linear independence in three dimensions
Linear independence in three dimensions
Linear independence in three dimensions
Linear subspaces
Linear subspaces
Linear subspaces
Spans as subspaces
Spans as subspaces
Spans as subspaces
Basis
Basis
Basis
BONUS! Extra practice problems. :)
24 Topics
Introduction to dot products and cross products
RESOURCE: Quiz solutions for this section
Dot products
Dot products
Dot products
Cauchy-Schwarz inequality
Cauchy-Schwarz inequality
Cauchy-Schwarz inequality
Vector triangle inequality
Vector triangle inequality
Vector triangle inequality
Angle between vectors
Angle between vectors
Angle between vectors
Equation of a plane and normal vectors
Equation of a plane and normal vectors
Equation of a plane and normal vectors
Cross products
Cross products
Cross products
Dot and cross products as opposite ideas
Dot and cross products as opposite ideas
Dot and cross products as opposite ideas
BONUS! Extra practice problems. :)
21 Topics
Introduction to matrix-vector products
RESOURCE: Quiz solutions for this section
Multiplying matrices by vectors
Multiplying matrices by vectors
Multiplying matrices by vectors
The null space and Ax=O
The null space and Ax=O
The null space and Ax=O
Null space of a matrix
Null space of a matrix
Null space of a matrix
The column space and Ax=b
The column space and Ax=b
The column space and Ax=b
Solving Ax=b
Solving Ax=b
Solving Ax=b
Dimensionality nullity and rank
Dimensionality nullity and rank
Dimensionality nullity and rank
BONUS! Extra practice problems. :)
27 Topics
Introduction to transformations
RESOURCE: Quiz solutions for this section
Functions and transformations
Functions and transformations
Functions and transformations
Transformation matrices and the image of the subset
Transformation matrices and the image of the subset
Transformation matrices and the image of the subset
Preimage image and the kernel
Preimage image and the kernel
Preimage image and the kernel
Linear transformations as matrix-vector products
Linear transformations as matrix-vector products
Linear transformations as matrix-vector products
Linear transformations as rotations
Linear transformations as rotations
Linear transformations as rotations
Adding and scaling linear transformations
Adding and scaling linear transformations
Adding and scaling linear transformations
Projections as linear transformations
Projections as linear transformations
Projections as linear transformations
Compositions of linear transformations
Compositions of linear transformations
Compositions of linear transformations
BONUS! Extra practice problems. :)
18 Topics
Introduction to inverses
RESOURCE: Quiz solutions for this section
Inverse of a transformation
Inverse of a transformation
Inverse of a transformation
Invertibility from the matrix-vector product
Invertibility from the matrix-vector product
Invertibility from the matrix-vector product
Inverse transformations are linear
Inverse transformations are linear
Inverse transformations are linear
Matrix inverses and invertible and singular matrices
Matrix inverses and invertible and singular matrices
Matrix inverses and invertible and singular matrices
Solving systems with inverse matrices
Solving systems with inverse matrices
Solving systems with inverse matrices
BONUS! Extra practice problems. :)
18 Topics
Introduction to determinants
RESOURCE: Quiz solutions for this section
Determinants
Determinants
Determinants
Cramer's rule for solving systems
Cramer's rule for solving systems
Cramer's rule for solving systems
Modifying determinants
Modifying determinants
Modifying determinants
Upper and lower triangular matrices
Upper and lower triangular matrices
Upper and lower triangular matrices
Using determinants to find area
Using determinants to find area
Using determinants to find area
BONUS! Extra practice problems. :)
18 Topics
Introduction to transposes
RESOURCE: Quiz solutions for this section
Transposes and their determinants
Transposes and their determinants
Transposes and their determinants
Transposes of products sums and inverses
Transposes of products sums and inverses
Transposes of products sums and inverses
Null and column spaces of the transpose
Null and column spaces of the transpose
Null and column spaces of the transpose
The product of a matrix and its transpose
The product of a matrix and its transpose
The product of a matrix and its transpose
A=LU factorization
A=LU factorization
A=LU factorization
BONUS! Extra practice problems. :)
21 Topics
Introduction to orthogonality and change of basis
RESOURCE: Quiz solutions for this section
Orthogonal complements
Orthogonal complements
Orthogonal complements
Orthogonal complements of the fundamental subspaces
Orthogonal complements of the fundamental subspaces
Orthogonal complements of the fundamental subspaces
Projection onto the subspace
Projection onto the subspace
Projection onto the subspace
Least squares solution
Least squares solution
Least squares solution
Coordinates in a new basis
Coordinates in a new basis
Coordinates in a new basis
Transformation matrix for a basis
Transformation matrix for a basis
Transformation matrix for a basis
BONUS! Extra practice problems. :)
12 Topics
Introduction to orthonormal bases and Gram-Schmidt
RESOURCE: Quiz solutions for this section
Orthonormal bases
Orthonormal bases
Orthonormal bases
Projection onto an orthonormal basis
Projection onto an orthonormal basis
Projection onto an orthonormal basis
Gram-Schmidt process for change of basis
Gram-Schmidt process for change of basis
Gram-Schmidt process for change of basis
BONUS! Extra practice problems. :)
9 Topics
Introduction to Eigenvalues and Eigenvectors
RESOURCE: Quiz solutions for this section
Eigenvalues eigenvectors eigenspaces
Eigenvalues eigenvectors eigenspaces
Eigenvalues eigenvectors eigenspaces
Eigen in three dimensions
Eigen in three dimensions
Eigen in three dimensions
BONUS! Extra practice problems. :)
4 Topics
Practice final exam #1 (optional)
Practice final exam #2 (optional)
Linear Algebra final exam
Wrap-up
Become a Linear Algebra Master
Related Linear Algebra Courses
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