-100%
Intermediate
Linear Algebra at College LEVEL III
Complex Vector Spaces, Jordan Theory, Matrix Polynomials …
$0.03
$30.00
Linear Algebra at College LEVEL III
What you'll learn
Complex Euclidean spaces and complex vector spaces.
Important classes of complex matrices: Hermitian, skew-Hermitian, and unitary.
Diagonalization, both orthogonal and unitary.
Jordan blocks and Jordan matrices as examples of non-diagonalizable cases.
How to compute the Jordan decomposition $A=QJQ^{−1}$ of a matrix.
Matrix powers and matrix polynomials, and methods for computing them.
The Cayley–Hamilton theorem and its applications.
-100%
Intermediate
Linear Algebra at College LEVEL II
Vector Spaces, Linear Transformations, Inner Product Spaces …
$0.02
$30.00
Linear Algebra at College LEVEL II
What you'll learn
Understand vector spaces as a generalization of Euclidean spaces.
Learn about bases and coordinates in vector spaces, similar to \(x,y,z\)-coordinates in 3-D space.
Develop skills to find a basis and express vectors in coordinates.
Study linear transformations and their matrix representations.
Explore the dot product, inner product, and the Gram–Schmidt process for a rectangular coordinate system in an inner product space.
Understand orthogonality and orthogonal matrices.
Free
Linear Algebra at Warm-Up LEVEL 0
What you'll learn
Definition and types of matrices (row, column, square, diagonal, identity, transpose, etc).
Matrix arithmetic (sum, subtraction, scalar multiplication, product, inversion).
Permutations and permutation matrices (transposition, cycle, and permutation).
The Euclidean spaces (with the sum and scalar multiplication).
Linear Transformations (Functions vs Linear transformations).
Determinants and their applications to lengths, areas, and volumes.
Importance of matrices in data representation and dimensionality reduction.
-100%
Intermediate
Linear Algebra at College LEVEL I
Matrices, Determinants, Diagonalization …
$0.01
$30.00
Linear Algebra at College LEVEL I
What you'll learn
Matrices for Systems of Linear Equations.
Elementary Operations, Elementary Matrices, and LU Decompositions.
Fundamental Properties of Determinants and Their Computation.
Leibniz formula and Cofactor expansions.
Eigenvalues and Eigenvectors, and their role in diagonalization.
Diagonalization and its application to linear recurrence relations (LRRs) and linear difference equations (LdEs).
