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What is the dot (Euclidean inner) product of two vectors?
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What is the dot (Euclidean inner) product of two vectors?What is the dot (Euclidean inner) product of two vectors? ...
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asked in Mathematics Jan 26
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Knowing the dot product of two vectors, how can I establish the angle between them?
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Find the dot product of the vectors shown in the diagram below
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image
Find the dot product of the vectors shown in the diagram below Find the dot product of the vectors shown in the diagram below   ...
by MathsGee Platinum
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asked in Mathematics Jan 26
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What is the component form of the dot product?
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What is the component form of the dot product?What is the component form of the dot product? ...
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asked in Mathematics Jan 26
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Which mathematician came up with the dot product notation?
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Which mathematician came up with the dot product notation?Which mathematician came up with the dot product notation? ...
by MathsGee Platinum
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asked in Mathematics Jan 26
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How do I calculate the dot product of two vectors?
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How do I calculate the dot product of two vectors?How do I calculate the dot product of two vectors? ...
by MathsGee Platinum
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asked in Mathematics Jan 26
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Calculate $\mathbf{u} \cdot \mathbf{v}$ for the following vectors in $R^{4}$ : $$ \mathbf{u}=(-1,3,5,7), \quad \mathbf{v}=(-3,-4,1,0) $$

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Find the angle between a diagonal of a cube and one of its edges
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Find the angle between a diagonal of a cube and one of its edgesFind the angle between a diagonal of a cube and one of its edges ...
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asked in Mathematics Jan 26
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What are the algebraic properties of the dot/inner product?
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What are the algebraic properties of the dot/inner product?What are the algebraic properties of the dot/inner product? ...
by MathsGee Platinum
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asked in Mathematics Jan 26
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If the product of two numbers is 1050 and their \(\mathrm{HCF}\) is 25 , find their LCM.
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If the product of two numbers is 1050 and their \(\mathrm{HCF}\) is 25 , find their LCM.If the product of two numbers is 1050 and their \(\mathrm{HCF}\) is 25 , find their LCM. ...
by MathsGee Platinum
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asked in Mathematics Jan 24
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List the prime factors of 60
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List the prime factors of 60List the prime factors of 60 ...
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asked in Mathematics Jan 24
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Let \(A\) be a positive definite \(n \times n\) real matrix, \(\vec{b}\) a real vector, and \(\vec{N}\) a real unit vector.
1 answer 7 views
Let \(A\) be a positive definite \(n \times n\) real matrix, \(\vec{b}\) a real vector, and \(\vec{N}\) a real unit vector.Let \(A\) be a positive definite \(n \times n\) real matrix, \(\vec{b}\) a real vector, and \(\vec{N}\) a real unit vector. a) For which value(s) of t ...
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asked in Mathematics Jan 21
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Find the function \(f \in \operatorname{span}\{1 \sin x, \cos x\}\) that minimizes \(\|\sin 2 x-f(x)\|\), where the norm comes from the inner product
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Let \(\mathcal{P}_{2}\) be the space of quadratic polynomials.
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Let \(\mathcal{P}_{2}\) be the space of quadratic polynomials.Let \(\mathcal{P}_{2}\) be the space of quadratic polynomials. a) Show that \(\langle f, g\rangle=f(-1) g(-1)+f(0) g(0)+f(1) g(1)\) is an inner produ ...
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asked in Mathematics Jan 21
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Proof or counterexample. Here \(v, w, z\) are vectors in a real inner product space \(H\).
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Proof or counterexample. Here \(v, w, z\) are vectors in a real inner product space \(H\).Proof or counterexample. Here \(v, w, z\) are vectors in a real inner product space \(H\). a) Let \(v, w, z\) be vectors in a real inner product space ...
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asked in Mathematics Jan 21
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Let \(\ell\) be any linear functional. Show there is a unique vector \(v \in \mathbb{R}^{n}\) so that \(\ell(x):=\langle x, v\rangle\).
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Let \(U, V, W\) be orthogonal vectors and let \(Z=a U+b V+c W\), where \(a, b, c\) are scalars.
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Let \(U, V, W\) be orthogonal vectors and let \(Z=a U+b V+c W\), where \(a, b, c\) are scalars.Let \(U, V, W\) be orthogonal vectors and let \(Z=a U+b V+c W\), where \(a, b, c\) are scalars. a) (Pythagoras) Show that \(\|Z\|^{2}=a^{2}\|U\|^{2}+b ...
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asked in Mathematics Jan 21
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Let \(V, W\) be vectors in \(\mathbb{R}^{n}\).
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Let \(V, W\) be vectors in \(\mathbb{R}^{n}\).Let \(V, W\) be vectors in \(\mathbb{R}^{n}\). a) Show that the Pythagorean relation \(\|V+W\|^{2}=\|V\|^{2}+\|W\|^{2}\) holds if and only if \(V\) a ...
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asked in Mathematics Jan 21
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Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .
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Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .   a) Find a basis for this space. b) Let \(D: \mathcal{P}_{2} \righta ...
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asked in Mathematics Jan 21
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If \(A\) and \(B\) are \(4 \times 4\) matrices such that \(\operatorname{rank}(A B)=3\), then \(\operatorname{rank}(B A)<4\).
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If \(A\) and \(B\) are \(4 \times 4\) matrices such that \(\operatorname{rank}(A B)=3\), then \(\operatorname{rank}(B A)<4\).For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE. There is no need to ju ...
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asked in Mathematics Jan 21
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent.
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent.Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent. a) For every \(y \in \mathbb{R}^{k}\) th ...
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asked in Mathematics Jan 20
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What are the rules of differentiation?
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What are the rules of differentiation?What are the rules of differentiation? ...
by MathsGee Platinum
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asked in Mathematics Jan 15
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Verify that the Cauchy-Schwarz inequality holds. \(\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)\)
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What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?
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What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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What is the dot product of u a row matrix and v a column matrix?
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What is the dot product of u a row matrix and v a column matrix?What is the dot product of u a row matrix and v a column matrix? ...
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asked in Mathematics Jan 13
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What is the dot product of u a column matrix and v a row matrix?
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What is the dot product of u a column matrix and v a row matrix?What is the dot product of u a column matrix and v a row matrix? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$
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Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy
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When are two nonzero vectors orthogonal to each other?
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When are two nonzero vectors orthogonal to each other?When are two nonzero vectors orthogonal to each other? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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