# Linear Algebra & Probability: Advanced Linear Algebra

Machine Learning    |    Intermediate
• 14 videos | 1h 42m 55s
• Includes Assessment
Learners will discover how to apply advanced linear algebra and its principles to derive machine learning implementations in this 14-video course. Explore PCA, tensors, decomposition, and singular-value decomposition, as well as how to reconstruct a rectangular matrix from singular-value decomposition. Key concepts covered here include how to use Python libraries to implement principal component analysis with matrix multiplication; sparse matrix and its operations; tensors in linear algebra and arithmetic operations that can be applied; and how to implement Hadamard product on tensors by using Python. Next, learn how to calculate singular-value decomposition and reconstruct a rectangular matrix; learn the characteristics of probability applicable in machine learning; and study probability in linear algebra and its role in machine learning. You will learn types of random variables and functions used to manage random numbers in probability; examine the concept and characteristics of central limit theorem and means and learn common usage scenarios; and examine the concept of parameter estimation and Gaussian distribution. Finally, learn the characteristics of binomial distribution with real-time examples.

## WHAT YOU WILL LEARN

• Discover the key concepts covered in this course Use python libraries to implement principal component analysis with matrix multiplication Describe sparse matrix and the operations that can be performed on sparse matrix Define the concept of tensors in linear algebra and list the arithmetic operations that can be applied on tensors Implement hadamard product on tensors using python Describe singular-value decomposition and how to calculate it Reconstruct a rectangular matrix from single-value decomposition
• Recognize the characteristics of probability that are applicable in machine learning Describe probability in linear algebra and its role in machine learning Recall the types of random variables and the functions that can be used to manage random numbers in probability Describe the concept and characteristics of central limit theorem and means and recognize common usage scenarios Describe parameter estimation and distribution using gaussian Describe binomial distribution and its characteristics Recall the arithmetic operations that can be applied on tensors, list the features of multivariate statistics that are applicable in machine learning, and implement hadamard product on tensors using python

## IN THIS COURSE

• In this video, you will use Python libraries to implement principal component analysis with matrix multiplication.
• 3.  Sparse Matrix
After completing this video, you will be able to describe a sparse matrix and the operations that can be performed on a sparse matrix.
• 4.  Tensor Arithmetic
Learn how to define the concept of tensors in linear algebra and list the arithmetic operations that can be applied to tensors.
• 5.  Hadamard Product and Tensors
In this video, learn how to implement the Hadamard product on tensors using Python.
• 6.  Singular-Value Decomposition
Upon completion of this video, you will be able to describe singular-value decomposition and how to compute it.
• 7.  Reconstruct Rectangular Matrix Using SVD
In this video, you will reconstruct a rectangular matrix from its single-value decomposition.
• 8.  Probability
Upon completion of this video, you will be able to recognize the characteristics of probability that are applicable in machine learning.
• 9.  Probability Basics and Propositions
After completing this video, you will be able to describe the role of probability in linear algebra and machine learning.
• 10.  Random Variable
After completing this video, you will be able to recall the types of random variables and the functions that can be used to generate random numbers in probability.
• 11.  Central Limit Theorem
Upon completion of this video, you will be able to describe the concept and characteristics of the central limit theorem and means and recognize common usage scenarios.
• 12.  Parameter Estimation and Gaussian Distribution
After completing this video, you will be able to describe parameter estimation and distribution using the Gaussian distribution.
• 13.  Binomial Distribution
After completing this video, you will be able to describe the binomial distribution and its characteristics.
• 14.  Exercise: Tensor Arithmetic and Hadamard Product
After completing this video, you will be able to recall the arithmetic operations that can be applied to tensors, list the features of multivariate statistics that are applicable in machine learning, and implement the Hadamard product on tensors using Python.

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