課程介紹

You need to learn linear algebra!

Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix

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哪些人適合這堂課？

• Anyone interested in learning about matrices and vectors
• Students who want supplemental instruction/practice for a linear algebra course
• Engineers who want to refresh their knowledge of matrices and decompositions
• Biologists who want to learn more about the math behind computational biology
• Data scientists (linear algebra is everywhere in data science!)
• Statisticians
• Someone who wants to know the important math underlying machine learning
• Someone who studied theoretical linear algebra and who wants to implement concepts in computers
• Computational scientists (statistics, biological, engineering, neuroscience, psychology, physics, etc.)
• Someone who wants to learn about eigendecomposition, diagonalization, and singular value decomposition!
• Artificial intelligence students

學習目標

• Understand theoretical concepts in linear algebra, including proofs
• Implement linear algebra concepts in scientific programming languages (MATLAB, Python)
• Apply linear algebra concepts to real datasets
• Ace your linear algebra exam!
• Apply linear algebra on computers with confidence
• Gain additional insights into solving problems in linear algebra, including homeworks and applications
• Be confident in learning advanced linear algebra topics
• Understand some of the important maths underlying machine learning
• The math underlying most of AI (artificial intelligence)

課程介紹

HOW BECOME A LINEAR ALGEBRA MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:

This 247-lesson course includes video and text explanations of everything from Linear Algebra, and it includes 69 quizzes (with solutions!) and an additional 12 workbooks wi

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哪些人適合這堂課？

• Current Linear Algebra students, or students about to start Linear Algebra who are looking to get ahead
• Anyone who wants to study math for fun after being away from school for a while
• Anyone who needs Linear Algebra as a prerequisite for Machine Learning, Deep Learning, Artificial Intelligence, Computer Programming, Computer Graphics and Animation, Data Analysis, etc.

學習目標

• 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

課程介紹

Have you ever wanted to fully understand the fourth dimension? How about the fifth? How about a space that is infinite dimensional? This is likely the most applicable mathematics course ever. We cover in depth everything about dots, lines, planes, sp

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哪些人適合這堂課？

• Potential Engineers
• Potential Mathematicians
• Those interested in Algebra

學習目標

• Solve linear systems
• Understand matrix algebra
• Know how to find the determinant of any matrix
• Understand vector spaces and their properties
• Understand what a basis is and how to apply it
• Understand linear transformations
• Understand eigenvectors
• Understand norms
• Understand inner products

課程介紹

This course is designed for university students taking intermediate algebra and college algebra and high school students taking algebra 1, algebra 2, or algebra 3.

Here is a list of topics covered in this course:

1.  Basic Arithmetic – Addition, Su

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哪些人適合這堂課？

• high school and college students including adults returning to college.

學習目標

• At the end of my course, students will be able to understand the basic fundamentals and principles of algebra.

課程介紹

From Matrix Calculus, To Robotics! From Control Systems, To Computer Graphics! From the Singular Value Decompositions to the Principal Component Analysis. From Systems Of Linear Equations, To Systems Of Differential Equations. From Inverses, to Pseud

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哪些人適合這堂課？

• Anyone Interested In Linear Algebra, especially, but not limited to, in the context of computer engineering, computer science, or data-science.
• Anyone Interested In Machine Learning & Deep learning.
• Anyone Interested In Computer Graphics & Game Development.
• Anyone Interested In Classical Control Systems & Robotics.
• Anyone Interested To know how to use python & matlab for Linear Algebra.
• Anyone Interested In Linear Algebra Theories, Concepts, And Proofs.

學習目標

• Gain Deep Understanding Of Linear Algebra Theoretically, Conceptually & Practically.
• Obtain A Very Robust Mathematical Foundation For Machine & Deep Learning, Computer Graphics, And Control Systems.
• Learn How To Use Both Python And Matlab For Solving & Visualizing Linear Algebra Problems.
• [Matrix Calculus] Learn How To Differentiate & Optimize Complex Equations Involving Matrices.
• Learn A Lot About Data Science, Co-variance Matrices, And The PCA.
• Learn About Linear Regression, The Normal Equation, And The Projection Matrix.
• Learn About Singular Value Decompositions Formally & Conceptually.
• Learn About Inverses And Pseudo Inverses.
• Learn About Determinants And Positive Definite Matrices.
• Learn How To Solve Systems Of Linear, Difference, & Differential Equations Both By Hand And Software.
• Learn About Lagrange Multipliers & Taylor Expansion.
• Learn About The Hessian Matrix And Its Importance In Multi-variable Calculus & Optimizations.
• Learn About Complex Transformation Matrices Like The Matrix To Perform Rotation Around An Arbitrary Axis In 3D.
• And Much More ! This is a 34+ hours course !

課程介紹

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The prerequisite to the course Linear Algebra for Beginners: Open Doors to Great Careers 2.

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哪些人適合這堂課？

• Working Professionals
• Anyone interested in gaining mastery of the core concepts in Linear Algebra.
• Adult Learners
• College Students

學習目標

• Refresh your math knowledge.
• Gain a firm foundation in Linear Algebra for furthering your career.
• Learn one of the mathematical subjects crucial for Computer Science.
• Learn one of the mathematical subjects crucial for engineering, computer science, physics, economics, computer animation, and cryptography among many others.
• Learn one of the mathematical subjects needed for Data Science.
• Learn a mathematical subject useful in becoming a Quant on Wall Street.

課程介紹

DO YOU WANT TO LEARN LINEAR ALGEBRA IN AN EASY WAY?

Great!

With 22+ hours of content and 200+ video lessons, this course covers everything in Linear Algebra, from start till the end!

Every concept is explained in simple language, and Quizzes and A

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哪些人適合這堂課？

• Students enrolled or planning to enroll in Linear Algebra class, and who want to excel in it
• Professionals who need a refresher in Math, especially Algebra and Linear Algebra
• Engineers, Scientists and Mathematicians who want to work with Linear Systems and Vector Spaces
• Anyone who wants to master Linear Algebra for Data Science, Data Analysis, Artificial Intelligence, Machine Learning, Deep Learning, Computer Graphics, Programming etc.

學習目標

• Fundamentals of Linear Algebra and how to ace your Linear Algebra exam
• Basics of matrices (notation, dimensions, types, addressing the entries etc.)
• Operations on a single matrix, e.g. scalar multiplication, transpose, determinant & adjoint
• Operations on two matrices, including addition, subtraction and multiplication of matrices
• Performing elementary row operations and finding Echelon Forms (REF & RREF)
• Inverses, including invertible and singular matrices, and the Cofactor method
• Solving systems of linear equations using matrices and inverse matrices, including Cramer’s rule to solve AX = B
• Properties of determinants, and how to perform Gauss-Jordan elimination
• Matrices as vectors, including vector addition and subtraction, Head-to-Tail rule, components, magnitude and midpoint of a vector
• Vector spaces, including dimensions, Euclidean spaces, closure properties and axioms
• Linear combinations and span, spanning set for a vector space and linear dependence
• Subspace and Null-space of a matrix, matrix-vector products
• Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
• Eigenvalues and Eigenvectors, including how to find Eigenvalues and the corresponding Eigenvectors
• Basic algebra concepts ( as a BONUS)
• And so much more…..

課程介紹

Interested in increasing your Machine Learning, Deep Learning expertise by effectively applying the mathematical skills?

Then, this course is for you.

With the growing learners of Machine Learning, Data Science, and Deep Learning.

The Common mista

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哪些人適合這堂課？

• Data Scientists who wish to improve their career in Data Science.
• Machine Learning Practitioners
• Any one who wants to understand the underpinnings of Maths in Data Science, Machine Learning and Artificial intelligence
• Any Data Science enthusiast
• Any student or professional who wants to start or transition to a career in Data Science.
• Students who want to refresh and learn important maths concepts required for Machine Learning , Deep Learning & Data Science.
• Any data analysts who want to level up in Machine Learning.
• Any people who are not satisfied with their job and who want to become a Data Scientist.

學習目標

• Build Mathematical intuition required for Data Science and Machine Learning
• The linear algebra intuition required to become a Data Scientist
• How to take their Data Science career to the next level
• Hacks, tips & tricks for their Data Science career
• Implement Machine Learning Algorithms better
• Apply Linear Algebra in Data Analysis
• Learn core concept to Implement in Machine Learning

課程介紹

What is this course all about?

Neuroscience (brain science) is changing — new brain-imaging technologies are allowing increasingly huge data sets, but analyzing the resulting Big Data is one of the biggest struggles in modern neuroscience (if don’t

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哪些人適合這堂課？

• Anyone interested in next-generation neuroscience data analyses
• Learners with interest in applied linear algebra to modern big-data challenges
• Neuroscientists dealing with “big data”
• Mathematicians, engineers, and physicists who are interested in learning about neuroscience data

學習目標

• Understand advanced linear algebra methods
• Apply advanced linear algebra methods in MATLAB
• Simulate multivariate data for testing analysis methods
• Analyzing multivariate time series datasets
• Appreciate the challenges neuroscientists are struggling with!
• Learn about modern neuroscience data analysis

課程介紹

接近40小時的線性代數課程，帶你一步步學會線性代數的重要觀念和公式，趕快收藏起來!!

線性代數為電腦科學、資訊工程等領域的必修課程，其應用之廣泛，包含機器學習、深度學習、預測模型、電腦圖形處理以及加密系統等等。這堂線性代數課程內容包含基本的線性方程組的基本運算、向量空間、線性獨立、矩陣的可逆性、行列式、施特拉森演算法、線性轉換、還有特徵矩陣以及特徵值的尋找，一步一步帶你認識所有重要的觀念、證明、運算過程與題目解答。不論你的數學基礎為何，都可以有系統性的認識線性代數中的重要理論、公式與計算原理。

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哪些人適合這堂課？

• 對電腦科學、資料科學與數學有興趣的開發者
• 正在大學就讀資訊工程、電腦科學、資料科學、理工科、數學的學生
• 對於演算法有興趣者
• 想要學習資料結構與演算法的人
• 不是資工本科系，但想要就讀或報考資工研究所的學生

學習目標

• 了解基本的矩陣原理，包含矩陣的運算與拆解
• 了解向量空間之間的線性轉換，包括轉換規則與數學應用
• 特徵向量以及特徵值的尋找(Eigenvectors and Eigenvalues)
• 了解並證明行列式(Determinant)的公式與計算規則
• 了解並證明可逆矩陣(Invertible Matrix)的性質與判斷方法
• 使用簡約列梯形式矩陣(Reduced Row Echelon Form)來找線性方程式的解
• 了解線性方程組當中的Free Variable and Basic Variable
• 向量的內積、外積、平行六面體、三階行列式的證明與計算
• 學習與分析矩陣乘法的施特拉森演算法(Strassen’s Algorithm)
• 秩零化度定理(Rank Theorem)
• 馬可夫鍊(Markov’s Chain)與線性代數的應用
• 使用Power Method and Shifted Inverse Power Method來逼近矩陣的特徵向量與特徵值
• 用Gershgorin circle theorem找出矩陣的特徵值在複數平面上的範圍
• 證明圖形理論當中的歐拉公式(Euler Formula)
• 了解向量空間中的正交(Orthogonality)與標準正交基(Orthonormal Basis)
• 分解矩陣，包含LU Decomposition, Diagonalization, QR Decomposition.
• 學會Grand-Schmidt Process
• 認識線性代數的Projection投影方法，並解決最小平方問題
• 認識與應用不同的內積空間 (Inner product space)