Linear Algebra Review and NumPy Basics1

Linear Algebra Review and NumPy Basics1

Chris J. Maddison

University of Toronto

1

Slides adapted from Ian Goodfellow¡¯s Deep Learning textbook lectures

Intro ML (UofT)

STA314-Tut02

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About this tutorial

Not a comprehensive survey of all of linear algebra.

Focused on the subset most relevant to machine learning.

Larger subset: e.g., Linear Algebra by Gilbert Strang

Intro ML (UofT)

STA314-Tut02

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Scalars

A scalar is a single number

Integers, real numbers, rational numbers, etc.

Typically denoted in italic font:

a, n, x

Intro ML (UofT)

STA314-Tut02

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Vectors

A vector is an array of d

numbers

xi be integer, real, binary, etc.

Notation to denote type and

size:

x ¡Ê Rd

Intro ML (UofT)

? ?

x1

? x2 ?

? ?

x =?.?

? .. ?

xd

STA314-Tut02

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Matrices

A matrix is an array of numbers

with two indices

Ai,j be integer, real, binary, etc.

Notation to denote type and

size:

A ¡Ê Rm¡Án

Intro ML (UofT)

STA314-Tut02



A

A1,2

A = 1,1

A2,1 A2,2



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