Matrices and Linear Algebra notes
16 notes by 9 users
This GoConqr page gathers over 16 community-made resources on Matrices and Linear Algebra notes: quizzes, mind maps, flashcards and notes to revise and practise with.
Select topic
- History of Matrices and Linear Algebra5
- Matrix Operations and Properties19
- Systems of Linear Equations11
- Row Reduction and Matrix Rank7
- Determinants14
- Inverse Matrices8
- Vector Spaces and Subspaces32
- Inner Product Spaces8
- Linear Transformations22
- Geometric Transformations7
- Eigenvalues and Eigenvectors11
- Matrix Decompositions and Canonical Forms6
Notes
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Matrices Notes Multiplication Finding The InverseThere is a formula which works whenever the determinant is not equal to 0 which allows us to find the inverse of a matrix.The determinant is ad-bc
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VECTOR SPACE - created from Mind Map Vectors in The Plane Vector Space Subspaces of Vector Space
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Introduction to Linear Algebra - created from Mind Map Linear Systems Matrices Properties of Matrix Operations
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Linear Transformation - created from Mind Map Introduction to Linear Transformation The Kernel and Range of A Linear Transformation The Matrix of Linear Transformation
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Diagonalization - created from Mind Map For the First Case Eigenvector Problem Matrix A is diagonalizable when A is similar to a diagonal matrix
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Eigenvalues & Eigenvectors - created from Mind Map Concepts Eigenspaces Finding Eigenvalues & Eigenvectors
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Linear Algebra - created from Mind Map Vector Space V is a vector space over a field F if there exists: - Addition operator, results in sum - Scalar multiplication, results in product If F is the real numbers (R) => Real Vector Space If F is...
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Matrices
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EIGENVALUES - created from Mind Map Possess can be used to compute determinants are related to
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Inner Products Space - created from Mind Map Vector Length & Unit Vectors Inner Products Space Orthogonal Basis
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Applications of Matrix Inverses to Coding Applications of Matrix Inverses to Coding A = 1 B = 2 C = 3 D = 4 E = 5 F = 6 G = 7 H = 8 I = 9 J = 10 K = 11 L = 12 M = 13 N = 14 O = 15 P = 16 Q = 17 R = 18 S = 19 T = 20 U = 21 V = 22 W = 23 X = 24 Y = 25 Z = 26 SP...
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Properties of Arithmetic with Vectors Summary of arithmetic with vectors: Proof for Rule 1-10
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MATH132 Week 9 Algebra - Elementary Matrices Revision: When solving linear systems, we learned that there are three basic classes of elementary row operation- Multiplying a row by a (nonzero) constant- Swap two rows- Add a mu...
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Hilbert Space
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INNER PRODUCT SPACE - created from Mind Map VECTOR LENGTH AND UNIT VECTOR DISTANCE BETWEEN TWO VECTOR ANGLE BETWEEN TWO VECTOR
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LINEAR TRANSFORMATION - created from Mind Map T(X)=AX TYPES OF LINEAR TRANSFORMATION THE KERNEL AND RANGE OF LINEAR TRANSFORMATION
More Matrices and Linear Algebra resources
About matrices and linear algebra notes
GoConqr OriginalUsing matrices and linear algebra notes
Start with Matrices Notes if you want to focus on multiplication and finding an inverse. It includes a formula for the inverse when the determinant is not zero. For a wider introduction, the notes on linear algebra cover linear systems, matrix operations, determinants and inverses.
Other notes move into vector spaces, eigenvalues and eigenvectors, diagonalization, and linear transformations. There are also notes on the arithmetic of vectors and on applications of matrix inverses to coding.
Plan your revision
Choose a topic from your course and read the relevant note. Write down the definitions or steps you want to remember, then return to the note to check them. For example, you could compare the material on inverses with the coding application.
When you want to check recall, switch to a quiz on the unit page. A mind map can help you revisit connections between topics. Pick a set of notes and work through a topic at your own pace.
Frequently asked questions
Which notes should I start with?
Matrices Notes is a useful starting point for multiplication and finding an inverse. If you want a broader introduction, the notes on linear algebra bring together linear systems, matrix operations, determinants and inverses. You can then move to a more specific topic in the list.
What topics do the notes cover?
The notes cover matrix multiplication and inverses, vector arithmetic, vector spaces, eigenvalues and eigenvectors, diagonalization, and linear transformations. Some explore specific applications, including coding with matrix inverses. Others introduce wider ideas, such as linear systems and the properties of matrix operations.
Are these notes free to use?
Yes. Every note listed here is free to open and study without an account. The resources were made by GoConqr users. A free account also lets you save quiz scores and make your own quizzes, mind maps, flashcards and notes.