Prove that if (mathbf{X}) is an (n times p) data matrix, then (operatorname{dVar}_{n}(a+) (b mathbf{X} C)=|b| operatorname{dar}_{n}(mathbf{X})),
Question:
Prove that if \(\mathbf{X}\) is an \(n \times p\) data matrix, then \(\operatorname{dVar}_{n}(a+\) \(b \mathbf{X} C)=|b| \operatorname{dar}_{n}(\mathbf{X})\), for all constant vectors \(a\) in \(\mathbb{R}^{p}\), scalars \(b\), and \(p \times p\) orthonormal matrices \(C\).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Answered By
Mahesh G
I have more than 7 years of experience in teaching physics, mathematics and python programming to more than 600 students including both online and offline tutoring.
I follow the following 7 step fundamental approach towards tutoring.
1. Curiosity, scope, enlightenment of the topic in hand.
2. Problem Definitions and elaboration.
3. Requisite mathematics, analytical abilities and quantitative
aptitude.
4. Preparing Algorithms for problem statement.
5. Concepts with analogies and building algorithm.
6. Introspection and improvising.
7. Daily class wise Cheat sheets(its not cheating) for consolidation.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Cases And Materials On Employment Law
ISBN: 9780199580712
8th Edition
Authors: Richard Painter, Ann Holmes
Question Posted:
Students also viewed these Social Science questions
-
In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...
-
(a) Use the following text to derive distributions for rat and chased. Use a five-word window, including open- and closed- class words, ignore case, punctuation and sentence boundaries and weight...
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
XY is a pharmaceutical company with the head-quarter in the United States. However, its cash flow depends only on sales in Japan. It receives a cash flow of Yen 20 billion with certainty in t=1. The...
-
A retired couple have $150,000 to invest and want to earn $15,000 per year in interest. The safer investment yields 9.5%, but they can supplement their earnings by investing some of their money at...
-
A recently graduated mechanical engineer wants to build a reserve fund as a safety net to pay his expenses in the unlikely event that an unexpected emergency arises. His aim is to have $45,000...
-
Comparative figures from the statement of financial position for Warder Ltd are shown below. Required (a) Prepare common size statements for the company for both years, and comment on what this...
-
The following data are for four independent process-costing departments. Inputs are added continuously. Required: Compute the equivalent units of production for each of the preceding departments...
-
Considerations: Positive counterclockwise direction of the moment. Modulus of section = 474 ???? 103 ????????3 Beam area: 5600 ????????2 ???????? = ???????? Height: 350 ???? General instruction...
-
Is it true that \(\operatorname{Cov}\left(\left|X-X^{\prime}ight|,\left|Y-Y^{\prime}ight|ight)=0\) implies that \(X\) and \(Y\) are independent? (Recall that \(X, X^{\prime}\) are iid; \(Y,...
-
Prove that \(\mathcal{V}_{n}(\mathbf{X})=0\) implies that all sample observations of \(\mathbf{X}\) are identical.
-
Xellnet provides ecommerce software for the pharmaceuticals industry. Xellnet is organized into several divisions. A companywide planning committee sets general strategy and goals for the company and...
-
How do disruptions in respiratory function contribute to pathological conditions such as respiratory acidosis, metabolic syndrome, and mitochondrial disorders?
-
Can you elucidate the role of molecular chaperones and protein quality control systems in maintaining the integrity and homeostasis of the cytoplasm, particularly under conditions of cellular stress...
-
Most math teachers have a very limited closet of clothing. They typically have three plaid shirts red, tan, and grey. They have two types of pants kaki and blue. They also only have 3 different...
-
Let F(n) be the Fibonacci function: F(0)=0 F(1) ====== = 1 F(n) F(n-1) + F(n-2) for n 2 n F(n+2) 1 for all n 0 Prove that F(i) = F(n+2). == - i=0
-
An element of a matrix is said to be "Saddle Point" if it is the strictly largest element (max) in its row and the strictly smallest element (min) in its column. For example, the matrix shown below...
-
Define incremental cash flow. (1) Should you subtract interest expense or dividends when calculating project cash flow? (2) Suppose the firm had spent $100,000 last year to rehabilitate the...
-
Open Text Corporation provides a suite of business information software products. Exhibit 10-9 contains Note 10 from the companys 2013 annual report detailing long-term debt. Required: a. Open Text...
-
Find expressions for the partial derivatives of the following functions: a. f(x,y) = f (g(x)k(y), g(x) + h(y) b. f(x,y,z) = f(g(+ y), h(y + z)) c. f(x,y,z) = f(xy, yz, zx) d. f(x,y) = f(x,g(x),...
-
Let f: Rn R. For x Rn, a. Show that Deif (a) = Dif (a).. b. Show that Dtxf (a) = Dxf(a).. c. If f is differentiable at , show that Dxf(a) = Df(a)(x) (a) and therefore Dx + yf(a) = Dxf (a) + Dyf (a)..
-
Let f be defined as in Problem 2-4. Show that Dxf (0, 0) exists for all , but if g 0, , then Dx + yf (0,0) =Dxf (00 Dx + y f (0, 0) = Dx f (0 , 0) + Dyf (0, 0) Is not true for all x and all y.
-
Image transcription text Heat Exchanger: Concentric Tube Connection: Parallel Ambient Temerature: 24 C Heater Tank Temperature: 60 C Cold Flow (m^3/s) Hot Flow (m^3/s) Cold Flow (L/min) Hot Flow...
-
Image transcription text Heat Exchanger: Concentric Tube Connection: Parallel Ambient Temerature: 24 C Heater Tank Temperature: 60 C Cold Flow (m*3/s) Cold Flow (L/min) Hot Flow (L/min) Hot Flow...
-
Figure 1d) Image transcription text 10 4 x )8.500 THRU All grooves are 8.5mm wide J (14.5005 10.000 unless otherwise indicated. 17.000 17.000 TOP VIEW 17.000 All 8.5mm grooves are 11mm deep. SCALE 1...
Study smarter with the SolutionInn App