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use inline MathML instead of converting to SVG first
saves the preprocessing step. fixes bad math rendering in PDF.
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Documents/Basics/ColumnVector.svg

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Documents/Basics/Tutorial 00.xml

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be (0, 2, 4); the X component is 0, the Y component is 2, and the Z component is 4. When
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writing them as part of an equation, they are written as follows:</para>
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<informalequation>
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<mediaobject>
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<imageobject>
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<imagedata fileref="ColumnVector.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="ColumnVector.mathml" />
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</informalequation>
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<para>In math equations, vector variables are either in boldface or written with an arrow
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over them.</para>
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components:</para>
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<equation>
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<title>Vector Addition with Numbers</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorAdditionNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorAdditionNum.mathml" />
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</equation>
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<para>Any operation where you perform an operation on each component of a vector is
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called a <glossterm>component-wise operation</glossterm>. Vector addition is
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<para>Numerically, this means negating each component of the vector.</para>
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<equation>
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<title>Vector Negation</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorNegationNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorNegationNum.mathml" />
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</equation>
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<para>Just as with scalar math, vector subtraction is the same as addition with the
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negation of the second vector.</para>
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vector addition.</para>
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<equation>
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<title>Vector Multiplication</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorMultiplicationNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorMultiplicationNum.mathml" />
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</equation>
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<formalpara>
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<title>Vector/Scalar Operations</title>
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vector is multiplied with each component of the scalar.</para>
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<equation>
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<title>Vector-Scalar Multiplication</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorScalarMultNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorScalarMultNum.mathml" />
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</equation>
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<para>Scalars can also be added to vectors. This, like vector-to-vector multiplication, has
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no geometric representation. It is a component-wise addition of the scalar with each
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component of the vector.</para>
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<equation>
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<title>Vector-Scalar Addition</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorScalarAddNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorScalarAddNum.mathml" />
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</equation>
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<formalpara>
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<title>Vector Algebra</title>
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and multiplication. They are commutative, associative, and distributive.</para>
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<equation>
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<title>Vector Algebra</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorMathProperties.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorMathProperties.mathml" />
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</equation>
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<para>Vector/scalar operations have similar properties.</para>
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<formalpara>
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<para>Numerically, computing the distance requires this equation:</para>
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<equation>
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<title>Vector Length</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorLengthNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorLengthNum.mathml" />
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</equation>
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<para>This uses the Pythagorean theorem to compute the length of the vector. This works for
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vectors of arbitrary dimensions, not just two or three.</para>
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reciprocal of the length.</para>
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<equation>
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<title>Vector Normalization</title>
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<mediaobject>
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<imageobject>
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<imagedata fileref="VectorNormalizationNum.svg"/>
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</imageobject>
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</mediaobject>
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<xi:include href="VectorNormalizationNum.mathml" />
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</equation>
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<para>This is not all of the vector math that we will use in these tutorials. New vector
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math operations will be introduced and explained as needed when they are first used. And

Documents/Basics/VectorAdditionNum.svg

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