# Linear Algebra for Core engineers and Data scientists

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This module is designed to address the GATE curriculum and build skills needed to solve every possible type of GATE situation. The module includes sub-modules  on higher order thinking and research aptitude. The higher order thinking and research aptitude submodules focus on transformation which is fundamental to advanced applications both in mechanical engineering and other disciplines (ex: robotics).

This short discussion helps you appreciate that every mathematical idea must have a physical basis. We most effectively demonstrate how tensor transformation is used physically appreciate principal quantities which are eigen values and vectors.

Sub-modules

• Holistic GATE Preparations
• Higher order of thinking
• Research aptitude

### Linear Algebra for Core engineers and Data scientists

#### Orthogonal transformation

• Generalised critical understanding of orthogonal transformation
• Concept of inverse using transformation
• INNOVENT’s problems on orthogonal transformation visited
• Gate 2006
• Gate 2009
• Gate 2019

#### Eigen values and Eigen vectors

• Numerical understanding of Eigenvalue and Eigenvectors visited
• Generalised understanding of Eigenvalue and Eigenvectors visited
• Numerical understanding of Eigenvectors
• Gate 1989 and 2008
• Gate 2012
• Gate 2006 and 2017
• Gate 2016
• Gate 2017
• Gate 2019
• Gate 2020

#### Solution of simultaneous of equations

• Critical concept understanding
• Generalised concept understanding
• Generalised concept understanding
• Gate 2019
• GATE 2019 (interpretation using Planes)
• Gate 2012

#### Properties of matrices

• Critical concept understanding
• Generalised concept understanding
• Generalised concept understanding
• Gate 2019
• GATE 2019 (interpretation using Planes)
• Gate 2012

#### Linearly independent and dependent vectors

• Generalised critical understanding of LI and LD vectors visited
• GATE relevant understanding visited
• GATE 2013
• GATE 2007
• GATE 2016

#### summary

• Critical concept understanding
• Eigenvalue and Eigenvectors visited
• Simultaneous equations
• Properties of determinants
• Property of matrices

#### Higher order of thinking

• Matrix as scaling and transforming agency
• Basic transformation – 1
• Basic transformation – 2
• Basic transformation – 3
• Combining basic transformations
• Trigonometric method to compute transformed area
• Vector method to compute transformed area
• Interpretation of Eigenvalue and vectors – Part 1
• Interpretation of Eigenvalue and vectors – Part 2
• Unit circle to ellipse transformation-1
• Unit circle to ellipse transformation-2
• Unit circle to ellipse transformation-3

#### Research aptitude

• Critical understanding of tensor transformation-1
• Critical understanding of tensor transformation-2
• Critical understanding of tensor transformation-3
• Critical Application to stress transformation
• Critical Application to inertia transformation

#### Mega case study

• Building transformation matrix using eigenvectors visited
• Diagonalisation using eigenvectors – 1
• Diagonalisation using eigenvectors – 2
• Mathematical interference – 1
• Mathematical interference – 2
• Mathematical interference -3
• Engineering example for eigenvalue repetition
• Common Doubts
• Summary

##### Course Features
 Lectures : Holistic GATE Preparations – [ 40] Higher order of thinking –[12 ] Research aptitude- Quizzes : yes Language : English Assessments : Yes Certificate of Completion : No Total time : Holistic GATE Preparations – [3hrs 12mins] Higher order of thinking – [55mins] Research aptitude – [1hr 28mins]
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