Ai Cheat Sheet
  • Home
  • Statistics ↓↑
    • Types of Measure
    • Population and Sample
    • Outliers
    • Variance
    • Standard Deviation
    • Skewness
    • Percentiles
    • Deciles
    • Quartiles
    • Box and Whisker Plots
    • Correlation and Covariance
    • Hypothesis Test
    • P Value
    • Statistical Significance
    • Bootstrapping
    • Confidence Interval
    • Central Limit Theorem
    • F1 Score (F Measure)
    • ROC and AUC
    • Random Variable
    • Expected Value
    • Central Limit Theorem
  • Probability ↓↑
    • What is Probability
    • Joint Probability
    • Marginal Probability
    • Conditional Probability
    • Bayesian Statistics
    • Naive Bayes
  • Data Science ↓↑
    • Probability Distribution
    • Bernoulli Distribution
    • Uniform Distribution
    • Binomial Distribution
    • Poisson Distribution
    • Normal Distribution
    • T-SNE
  • Data Engineering ↓↑
    • Data Science vs Data Engineering
    • Data Architecture
    • Data Governance
    • Data Quality
    • Data Compliance
    • Business Intelligence
    • Data Modeling
    • Data Catalog
    • Data Cleaning
    • Data Format
      • Apache Avro
    • Tools
      • Data Fusion
      • Dataflow
      • Dataproc
      • BigQuery
    • Cloud Platforms
      • GCP
    • SQL
      • ACID
      • SQL Transaction
      • Query Optimization
    • Data Engineering Interview Questions
  • Vector and Matrix
    • Vector
    • Matrix
  • Machine Learning ↓↑
    • L1 and L2 Loss Function
    • Linear Regression
    • Logistic Regression
    • Naive Bayes Classifier
    • Resources
  • Deep Learning ↓↑
    • Neural Networks and Deep Learning
    • Improving Deep Neural Networks
    • Structuring Machine Learning Projects
    • Convolutional Neural Networks
    • Sequence Models
    • Bias
    • Activation Function
    • Softmax
    • Cross Entropy
  • Natural Language Processing ↓↑
    • Linguistics and NLP
    • Text Augmentation
    • CNN for NLP
    • Transformers
      • Implementation
  • Computer Vision ↓↑
    • Object Localization
    • Object Detection
    • Bounding Box Prediction
    • Evaluating Object Localization
    • Anchor Boxes
    • YOLO Algorithm
    • R-CNN
    • Face Recognition
  • Time Series
    • Resources
  • Reinforcement Learning
    • Reinforcement Learning
  • System Design
    • SW Diagramming
    • Feed
  • Tools
    • PyTorch
    • Tensorflow
    • Hugging Face
  • MLOps
    • Vertex AI
      • Dataset
      • Feature Store
      • Pipelines
      • Training
      • Experiments
      • Model Registry
      • Serving
        • Batch Predictions
        • Online Predictions
      • Metadata
      • Matching Engine
      • Monitoring and Alerting
  • Interview Questions ↓↑
    • Questions by Shared Experience
  • Contact
    • My Personal Website
Powered by GitBook
On this page
  • Matrix Multiplication
  • Multiplying a Matrix by Another Matrix
  • Dividing a Matrix by Another Matrix
  • Inverse of a Matrix
  • Determinant of a Matrix
  • Identity Matrix

Was this helpful?

  1. Vector and Matrix

Matrix

PreviousVectorNextL1 and L2 Loss Function

Last updated 4 years ago

Was this helpful?

Matrix Multiplication

Hadamard Product/Multiplication is simply the elementwise multiplication of two Matrix. Usually, in programming, the notation of this operation is a star (*).

Multiplying a Matrix by Another Matrix

Need to do the "dot product" of rows and columns.

Dividing a Matrix by Another Matrix

We don't do that. Rather we make the inverse of the denominator matrix and then multiply it with the numerator matrix.

However, the elementwise division is obviously possible.

Inverse of a Matrix

2x2 Matrix. The inverse of a 2x2 is easy compared to larger matrices (such as a 3x3, 4x4, etc). For those larger matrices there are other methods to work out the inverse.

Very much helpful if we want to get an unknown matrix such as X where,XA=BXA = BXA=B by X=BA−1X = BA^{-1}X=BA−1

Determinant of a Matrix

The determinant of a matrix is a special number that can be calculated from a square matrix. The determinant helps us find the inverse of a matrix, tells us things about the matrix that are useful in systems of linear equations, calculus and more.

Calculating the Determinant - For a 2×2 Matrix

∣A∣=ad−bc|A| = ad - bc∣A∣=ad−bc

Identity Matrix

It is the matrix equivalent of the number "1". It is "square" (has same number of rows as columns), It has 1s on the diagonal and 0s everywhere else.

A×A−1=A−1×A=IA \times A^{-1} = A^{-1} \times A = I A×A−1=A−1×A=I

How to Multiply Matrices
Logo
Inverse of a Matrix
Logo