Argomenti correlati
Il corso include
- 10 h 50 min di video
- 84 lezioni
- Livello: Principiante
- Lingua: English
- Ricordiamo dove eri arrivato
- Del tutto gratis, senza carta
Lezioni
9 sezioni · 84 lezioni · 10 h 50 min durata totale
Lezioni 1–1010 lezioni · 1 h 25 min
- What's the big idea of Linear Algebra? **Course Intro**13 min
- What is a Solution to a Linear System? **Intro**5 min
- Visualizing Solutions to Linear Systems - - 2D & 3D Cases Geometrically8 min
- Rewriting a Linear System using Matrix Notation3 min
- Using Elementary Row Operations to Solve Systems of Linear Equations7 min
- Using Elementary Row Operations to simplify a linear system10 min
- Examples with 0, 1, and infinitely many solutions to linear systems7 min
- Row Echelon Form and Reduced Row Echelon Form7 min
- Back Substitution with infinitely many solutions11 min
- The Gaussian Algorithm Visualized14 min
Lezioni 11–2010 lezioni · 1 h 14 min
- What is a vector? Visualizing Vector Addition & Scalar Multiplication7 min
- Introducing Linear Combinations & Span10 min
- How to determine if one vector is in the span of other vectors?5 min
- Matrix-Vector Multiplication and the equation Ax=b7 min
- Matrix-Vector Multiplication Example5 min
- Proving Algebraic Rules in Linear Algebra --- Ex: A(b+c) = Ab +Ac8 min
- The Big Theorem, Part I14 min
- Writing solutions to Ax=b in vector form5 min
- Geometric View on Solutions to Ax=b and Ax=0.6 min
- Three nice properties of homogeneous systems of linear equations8 min
Lezioni 21–3010 lezioni · 1 h 12 min
- Linear Dependence and Independence - Geometrically8 min
- Determining Linear Independence vs Linear Dependence7 min
- Making a Math Concept Map | Ex: Linear Independence7 min
- Transformations and Matrix Transformations5 min
- Three examples of Matrix Transformations8 min
- Linear Transformations8 min
- Are Matrix Transformations and Linear Transformation the same? Part I3 min
- Every vector is a linear combination of the same n simple vectors!7 min
- Matrix Transformations are the same thing as Linear Transformations9 min
- Finding the Matrix of a Linear Transformation9 min
Lezioni 31–4010 lezioni · 1 h 20 min
- One-to-one, Onto, and the Big Theorem Part II10 min
- The motivation and definition of Matrix Multiplication10 min
- Computing matrix multiplication6 min
- Visualizing Composition of Linear Transformations **aka Matrix Multiplication**14 min
- Elementary Matrices7 min
- You can "invert" matrices to solve equations...sometimes!7 min
- Finding inverses to 2x2 matrices is easy!3 min
- Find the Inverse of a Matrix7 min
- When does a matrix fail to be invertible? Also more "Big Theorem".9 min
- Visualizing Invertible Transformations (plus why we need one-to-one)8 min
Lezioni 41–5010 lezioni · 1 h 16 min
- Invertible Matrices correspond with Invertible Transformations **proof**7 min
- Determinants - a "quick" computation to tell if a matrix is invertible9 min
- Determinants can be computed along any row or column - choose the easiest!4 min
- Vector Spaces | Definition & Examples8 min
- The Vector Space of Polynomials: Span, Linear Independence, and Basis13 min
- Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples6 min
- The Span is a Subspace | Proof + Visualization5 min
- The Null Space & Column Space of a Matrix | Algebraically & Geometrically11 min
- The Basis of a Subspace4 min
- Finding a Basis for the Nullspace or Column space of a matrix A10 min
Lezioni 51–6010 lezioni · 56 min
- Finding a basis for Col(A) when A is not in REF form.3 min
- Coordinate Systems From Non-Standard Bases | Definitions + Visualization7 min
- Writing Vectors in a New Coordinate System **Example**4 min
- What Exactly are Grid Lines in Coordinate Systems?5 min
- The Dimension of a Subspace | Definition + First Examples5 min
- Computing Dimension of Null Space & Column Space3 min
- The Dimension Theorem | Dim(Null(A)) + Dim(Col(A)) = n | Also, Rank!4 min
- Changing Between Two Bases | Derivation + Example8 min
- Visualizing Change Of Basis Dynamically8 min
- Example: Writing a vector in a new basis9 min
Lezioni 61–7010 lezioni · 1 h 22 min
- What eigenvalues and eigenvectors mean geometrically9 min
- Using determinants to compute eigenvalues & eigenvectors5 min
- Example: Computing Eigenvalues and Eigenvectors8 min
- A range of possibilities for eigenvalues and eigenvectors10 min
- Diagonal Matrices are Freaking Awesome6 min
- How the Diagonalization Process Works8 min
- Compute large powers of a matrix via diagonalization3 min
- Full Example: Diagonalizing a Matrix10 min
- COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**14 min
- Visualizing Diagonalization & Eigenbases10 min
Lezioni 71–8010 lezioni · 1 h 24 min
- Similar matrices have similar properties9 min
- The Similarity Relationship Represents a Change of Basis10 min
- Dot Products and Length7 min
- Distance, Angles, Orthogonality and Pythagoras for vectors8 min
- Orthogonal bases are easy to work with!5 min
- Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Complement4 min
- The geometric view on orthogonal projections11 min
- Orthogonal Decomposition Theorem Part II11 min
- Proving that orthogonal projections are a form of minimization7 min
- Using Gram-Schmidt to orthogonalize a basis11 min
Cosa serve
- Nessuna esperienza richiesta: il corso parte da zero.
Descrizione
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
A chi è rivolto
- Chi inizia con Scienze da zero.
Questi due punti sono una nostra lettura del livello. La descrizione è dell'autore.