# Recent questions tagged product

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Let $W$ be a linear space with an inner product and $A: W \rightarrow W$ be a linear map whose image is one dimensional (so in the case of matrices, it has rank one).
Let $W$ be a linear space with an inner product and $A: W \rightarrow W$ be a linear map whose image is one dimensional (so in the case of matrices, it has rank one).Let $W$ be a linear space with an inner product and $A: W \rightarrow W$ be a linear map whose image is one dimensional (so in the case of matrice ...
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Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \vec{v}=\vec{w}$ and $R \vec{w}=\vec{v}$.Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \v ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 .Let $\mathcal{P}_{2}$ be the space of polynomials of degree at most 2 . &nbsp; a) Find a basis for this space. b) Let $D: \mathcal{P}_{2} \righta ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \(\mathcal{P}_{1}$ be the linear space of real polynomials of degree at most one, so a typical element is $p(x):=a+b x$, where $a$ and $b$ are real numbers.
Let $\mathcal{P}_{1}$ be the linear space of real polynomials of degree at most one, so a typical element is $p(x):=a+b x$, where $a$ and $b$ are real numbers.Let $\mathcal{P}_{1}$ be the linear space of real polynomials of degree at most one, so a typical element is $p(x):=a+b x$, where $a$ and $b$ ...
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If $A$ and $B$ are $4 \times 4$ matrices such that $\operatorname{rank}(A B)=3$, then $\operatorname{rank}(B A)<4$.
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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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.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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Let $\mathcal{P}_{k}$ be the space of polynomials of degree at most $k$ and define the linear map $L: \mathcal{P}_{k} \rightarrow \mathcal{P}_{k+1}$ by $L p:=p^{\prime \prime}(x)+x p(x) .$Let $\mathcal{P}_{k}$ be the space of polynomials of degree at most $k$ and define the linear map $L: \mathcal{P}_{k} \rightarrow \mathcal{P}_{k+ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What are the rules of differentiation? 1 answer 5 views What are the rules of differentiation?What are the rules of differentiation? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Verify that the Cauchy-Schwarz inequality holds. \(\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
Verify that the Cauchy-Schwarz inequality holds. $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$Verify that the Cauchy-Schwarz inequality holds. (b) $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$ ...
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What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?
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? ...
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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?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 column matrix and v a row matrix?
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? ...
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$Verify that the Cauchy&amp;ndash;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 $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$Verify that the Cauchy&amp;ndash;Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$ ...
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$Verify that the Cauchy&amp;ndash;Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$ ...
Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y)$ that satisfy the stated condition.Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfy 0 answers 9 views Show that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfyShow that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfy $$\cos \ ... close 0 answers 102 views Let \mathbf{u} be a vector in R^{100} whose i th component is i, and let \mathbf{v} be the vector in R^{100} whose i th component is 1 /(i+1). Find the dot product of \mathbf{u} and \mathbf{v}.Let \mathbf{u} be a vector in R^{100} whose i th component is i, and let \mathbf{v} be the vector in R^{100} whose i th component is 1 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 When are two nonzero vectors orthogonal to each other? 1 answer 20 views When are two nonzero vectors orthogonal to each other?When are two nonzero vectors orthogonal to each other? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What are Orthogonal Projections? 1 answer 7 views What are Orthogonal Projections?What are Orthogonal Projections? ... close 1 answer 6 views If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} $$If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}= ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\mathbf{v}=(a, b)$and$\mathbf{w}=(-b, a)$are orthogonal vectors. 0 answers 4 views Show that$\mathbf{v}=(a, b)$and$\mathbf{w}=(-b, a)$are orthogonal vectors.Show that$\mathbf{v}=(a, b)$and$\mathbf{w}=(-b, a)$are orthogonal vectors. ... close 0 answers 6 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the dot product of u a row matrix and v a row matrix? 1 answer 4 views What is the dot product of u a row matrix and v a row matrix?What is the dot product of u a row matrix and v a row matrix? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false? 0 answers 7 views Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false?Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false? A.$-a \time ...