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Что входит в курс
- 10 ч 50 мин видео
- 84 уроков
- Уровень: Начальный
- Язык: English
- Помним, где вы остановились
- Полностью бесплатно, без карты
Уроки
9 разделов · 84 урока · 10 ч 50 мин общая длительность
Уроки 1–1010 уроков · 1 ч 25 мин
- What's the big idea of Linear Algebra? **Course Intro**13 мин
- What is a Solution to a Linear System? **Intro**5 мин
- Visualizing Solutions to Linear Systems - - 2D & 3D Cases Geometrically8 мин
- Rewriting a Linear System using Matrix Notation3 мин
- Using Elementary Row Operations to Solve Systems of Linear Equations7 мин
- Using Elementary Row Operations to simplify a linear system10 мин
- Examples with 0, 1, and infinitely many solutions to linear systems7 мин
- Row Echelon Form and Reduced Row Echelon Form7 мин
- Back Substitution with infinitely many solutions11 мин
- The Gaussian Algorithm Visualized14 мин
Уроки 11–2010 уроков · 1 ч 14 мин
- What is a vector? Visualizing Vector Addition & Scalar Multiplication7 мин
- Introducing Linear Combinations & Span10 мин
- How to determine if one vector is in the span of other vectors?5 мин
- Matrix-Vector Multiplication and the equation Ax=b7 мин
- Matrix-Vector Multiplication Example5 мин
- Proving Algebraic Rules in Linear Algebra --- Ex: A(b+c) = Ab +Ac8 мин
- The Big Theorem, Part I14 мин
- Writing solutions to Ax=b in vector form5 мин
- Geometric View on Solutions to Ax=b and Ax=0.6 мин
- Three nice properties of homogeneous systems of linear equations8 мин
Уроки 21–3010 уроков · 1 ч 12 мин
- Linear Dependence and Independence - Geometrically8 мин
- Determining Linear Independence vs Linear Dependence7 мин
- Making a Math Concept Map | Ex: Linear Independence7 мин
- Transformations and Matrix Transformations5 мин
- Three examples of Matrix Transformations8 мин
- Linear Transformations8 мин
- Are Matrix Transformations and Linear Transformation the same? Part I3 мин
- Every vector is a linear combination of the same n simple vectors!7 мин
- Matrix Transformations are the same thing as Linear Transformations9 мин
- Finding the Matrix of a Linear Transformation9 мин
Уроки 31–4010 уроков · 1 ч 20 мин
- One-to-one, Onto, and the Big Theorem Part II10 мин
- The motivation and definition of Matrix Multiplication10 мин
- Computing matrix multiplication6 мин
- Visualizing Composition of Linear Transformations **aka Matrix Multiplication**14 мин
- Elementary Matrices7 мин
- You can "invert" matrices to solve equations...sometimes!7 мин
- Finding inverses to 2x2 matrices is easy!3 мин
- Find the Inverse of a Matrix7 мин
- When does a matrix fail to be invertible? Also more "Big Theorem".9 мин
- Visualizing Invertible Transformations (plus why we need one-to-one)8 мин
Уроки 41–5010 уроков · 1 ч 16 мин
- Invertible Matrices correspond with Invertible Transformations **proof**7 мин
- Determinants - a "quick" computation to tell if a matrix is invertible9 мин
- Determinants can be computed along any row or column - choose the easiest!4 мин
- Vector Spaces | Definition & Examples8 мин
- The Vector Space of Polynomials: Span, Linear Independence, and Basis13 мин
- Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples6 мин
- The Span is a Subspace | Proof + Visualization5 мин
- The Null Space & Column Space of a Matrix | Algebraically & Geometrically11 мин
- The Basis of a Subspace4 мин
- Finding a Basis for the Nullspace or Column space of a matrix A10 мин
Уроки 51–6010 уроков · 56 мин
- Finding a basis for Col(A) when A is not in REF form.3 мин
- Coordinate Systems From Non-Standard Bases | Definitions + Visualization7 мин
- Writing Vectors in a New Coordinate System **Example**4 мин
- What Exactly are Grid Lines in Coordinate Systems?5 мин
- The Dimension of a Subspace | Definition + First Examples5 мин
- Computing Dimension of Null Space & Column Space3 мин
- The Dimension Theorem | Dim(Null(A)) + Dim(Col(A)) = n | Also, Rank!4 мин
- Changing Between Two Bases | Derivation + Example8 мин
- Visualizing Change Of Basis Dynamically8 мин
- Example: Writing a vector in a new basis9 мин
Уроки 61–7010 уроков · 1 ч 22 мин
- What eigenvalues and eigenvectors mean geometrically9 мин
- Using determinants to compute eigenvalues & eigenvectors5 мин
- Example: Computing Eigenvalues and Eigenvectors8 мин
- A range of possibilities for eigenvalues and eigenvectors10 мин
- Diagonal Matrices are Freaking Awesome6 мин
- How the Diagonalization Process Works8 мин
- Compute large powers of a matrix via diagonalization3 мин
- Full Example: Diagonalizing a Matrix10 мин
- COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**14 мин
- Visualizing Diagonalization & Eigenbases10 мин
Уроки 71–8010 уроков · 1 ч 24 мин
- Similar matrices have similar properties9 мин
- The Similarity Relationship Represents a Change of Basis10 мин
- Dot Products and Length7 мин
- Distance, Angles, Orthogonality and Pythagoras for vectors8 мин
- Orthogonal bases are easy to work with!5 мин
- Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Complement4 мин
- The geometric view on orthogonal projections11 мин
- Orthogonal Decomposition Theorem Part II11 мин
- Proving that orthogonal projections are a form of minimization7 мин
- Using Gram-Schmidt to orthogonalize a basis11 мин
Что нужно
- Опыт не нужен: курс начинается с нуля.
Описание
A one semester, introductory course in Linear Algebra. Emphasizes both conceptual understanding and procedural fluency in applying the techniques of Linear Algebra. Major topics are solving linear systems, linear transformations, linear independence, bases, dimension, eigenvalues and eigenvectors, diagonalization, orthogonality and Gram-Schmidt
Кому подойдёт курс
- Тем, кто начинает Наука с нуля.
Эти два пункта — наш вывод из уровня курса. Описание принадлежит автору.