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Matrix Methods
  • Level Professional
  • المدة 7 ساعات hours
  • الطبع بواسطة University of Minnesota
  • Offered by

عن

Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction. Optional examples using Python are used to illustrate the concepts and allow the learner to experiment with the algorithms.

الوحدات

Linear Relations expressed as Matrix Multiplication.

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Matrix

1 Videos

  • Matrix: Tabular Data

1 Readings

  • Vector and Matrix operations

Matrix Multiplication and Combinations

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Linear combinations

2 Videos

  • Matrix Multiplication
  • Supplement: Matrices in Python/Numpy

1 Readings

  • Matrix Multiplication

Assignment 1

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1 Assignment

  • Matrix Combinations

Matrix-Matrix Multiplication and other Matrix Operations

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Matrix Operations

1 Videos

  • Matrix as Mathematical Objects

1 Readings

  • Matrix Arithmetic

Matrix Transpose

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Matrix Transpose

2 Videos

  • Matrix Transpose
  • Supplement: Matrix Transpose in Python

1 Readings

  • Matrix Transpose

Assignment 2

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1 Assignment

  • Matrix Multiplication and Other Operations

Setup and solve a system of linear equations

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    • 1 Readings
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1 Assignment

  • Systems of Linear Equations

1 Videos

  • Systems of Linear Equations

1 Readings

  • Systems of Linear Equations

Gauss Elimination in Matrix Notation

    • 1 Videos
    • 1 Readings
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1 Assignment

  • Solution of Linear Equations via Elimination

1 Videos

  • Solution of Linear Equations via Elimination

1 Readings

  • Gaussian Elimination Algorithm

LU Decomposition

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • LU Decomposition

2 Videos

  • LU Decomposition: Matrix is a Product of Simple Matrices
  • Supplement: Solve Linear Equations in Python

1 Readings

  • LU Decomposition

Assignment 3

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1 Assignment

  • Systems of linear equations

Orthogonality

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Orthogonality and Inner Product

1 Videos

  • Orthogonality and Inner Product.

1 Readings

  • Orthogonality and the Inner Product

Overdetermined System: Best approximation

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Linear Least Squares

1 Videos

  • Linear Least Squares: Best Approximation

1 Readings

  • Linear Least Squares

Best Approximation equals Orthogonality leads to Normal Equations

    • 1 Videos
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1 Assignment

  • Normal equations

1 Videos

  • Least Distance -> Orthogonality -> Normal Equations

Example: Approximate Curve Fitting

    • 1 Videos
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1 Assignment

  • Approximate Curve Fitting

1 Videos

  • Example: Approximate Curve Fitting

Assignment 4

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1 Assignment

  • Linear Least Squares

SVD as a Decomposition

    • 1 Readings
    • 1 Assignment
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1 Assignment

  • SVD as a Decomposition

1 Readings

  • S V D

SVD as a Data Analytics Tool

    • 1 Readings
    • 1 Assignment
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1 Assignment

  • SVD as a Data Analytics Tool

1 Readings

  • Latent Semantic Indexing

Assignment 5

    • 1 Assignment
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1 Assignment

  • Singular Value Decomposition

Auto Summary

Elevate your understanding of machine learning and data analysis with the "Matrix Methods" course, a comprehensive dive into the essential mathematical techniques pivotal for handling tabular data. This professional-level course, offered by Coursera, is meticulously designed for those looking to master the foundational elements of Matrix Methods. Spanning 420 minutes, it covers critical topics such as matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Learners will also explore the powerful Singular Value Decomposition, essential for dimensionality reduction, Principal Component Analysis, and noise reduction. To enhance understanding and practical application, optional Python examples are incorporated, allowing participants to experiment with the algorithms in real-time. Ideal for professionals aiming to deepen their expertise in Maths & Statistics, this course offers flexible learning through a Starter subscription. Join now to unlock the potential of Matrix Methods and advance your analytical skills in machine learning and data analysis.

Daniel Boley
Instructor

Daniel Boley