CS1371 Computing for Engineers

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CS1371 Computing for Engineers

• Lecture 4
• Arrays/Matrices

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(No Transcript)
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What should you should know now

• How to start(and stop) Matlab
• Basic operations and trix! (Up arrow,etc.)
• How to do simple calculations in the command
  window
• How to create, edit and run scripts
• Basic vector operations
• Creation
• Addition/Subtraction/Multiplications/etc.
• Element by element operations
• Slicing
• Logic operations

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This Week

• Today
• Basic Arrays/Matrices
• Conditionals
• Thursday
• Functions

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Arrays and Matrices

• Vectors -gt Arrays -gt Matrices
• Two-dimensional

Jagged arraywe Wont use these!
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Properties

• sz size(array)
• rows, cols size(array)
• length(array)
• transpose '

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Properties

• Special cases
• Square
• Diagonal
• row vector/column vector

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Array Creation

• Direct entry with semicolons () separating rows
• still works!
• zeros, one, rand, diag, magic

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Array Access

• Retrieving/Storing/Removing
• Matlabs dirty little secret

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Array Operations

• Arithmetic
• Scaler ops (. ./ .)
• Matrix ops
• Logical
• Concatenation
• Slicing

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Slicing

• B(ltrangex1gt,ltrangey1) A(ltrangex2gt, ltrangey2gt)

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Matrices

• Arthur Cayley (1821-1895)
• Inventor of Matrices
• "When Cayley invented matrices in the late 19th
  century he was proud of the fact that they were
  absolutely useless. " - Steven Krantz
  Mathematician Washington University

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Matlab Excels in Matrix Operations

• This separates Matlab from high-level languages
  like C, FORTRAN, etc.
• Some operations supported
• A' transpose of A
• inv(A) inverse of the matrix
• det(A) determinant of the matrix
• rank(A) rank of the matrix
• trace(A) sum of diagonal terms
• sqrtm(A) matrix square root
• (i.e., if Bsqrtm(A), then ABB)
• norm(A) matrix norm (useful for vector
  magnitudes)
• eig(A) eigenvalues and eigenvectors of matrix

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But who cares?

• A large and very useful area of mathematics deals
  with what is called linear algebra and matrices
  are an integral part of this.
• Many advanced computational methods in
  engineering make extensive use of linear algebra,
  and hence of matrices

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Example Simultaneous Equations
This is what is contained
This is what You buy
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Targets
Batch Size 100 kilograms
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Unknowns

• w - kg of Feldspar
• x kg of Diatomite
• y kg of Magnesite
• z kg of Talc

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How much silica will we have?
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How much silica will we have?
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What is the constraint?
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Set of Simultaneous Equations
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Expressing in Matrix Format
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Two ways to solve

• Using the Inverse
• Ax b

• Using matrix division
• Ax b