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Common matrix diagrams are LType, TType, XType, and YType LType Matrix Diagram What is an LType Matrix Chart?We could of course have simply written the above description as two separate but coupled firstorder differential equations with constant coefficientsWhen studying an actual control system block diagram, we wish to select the ppyhysical variables as state variables For example, the block diagram of an open loop DC motor is 1 1 1 5 5 − − s s 1 1 1 2 − − s s 1 1 1 3 6 − − s s We draw the signal‐flow diagraph of each block separately and then connect them We select x 1

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L t y x c matrix diagram

L t y x c matrix diagram-F X → Y from a set X to a set Y associates to each x ∈ X a unique element f(x) ∈ Y Following is some commonly used terminologies 1 X is called the domain of f 2 Y is called the codomain of f 3 If f(x) = y, then we say y is the image of x The preimage of y is preimage(y) = {x ∈ X f(x) = y} 4In the examples, matrix axes have been shaded to emphasize the letter that gives each matrix its name An L–shaped matrix relates two groups of items to each other (or one group to itself) A T–shaped matrix relates three groups of items groups B and C are each related to A Groups B and C are not related to each other A Y–shaped matrix relates three groups of items

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Faces ¶ The faces are the complementary regions of the link diagram Each face is given as a list of corners of crossings as one goes around clockwiseThese corners are recorded as CrossingStrands, where CrossingStrand(c, j) denotes the corner of the face abutting crossing c between strand j and j 1, Rޯ * 0 i懇 Yd# k 3gμhݺu t 2 J K 'rDh޸ m{% }Ľ < L&s r% è;As in 3 We let l be the line perpendicular to U through the origin l (and thus U) α=30D =U⊥ =l⊥ 9 3 The task is to calculate with the standard basis E of , for the two rotations about the axis through the angle TE l \3 T\\3→ α=30D To do this, use the work in 3 Recipe Calculate a unit vector that lies in the line

" X_ v ڗ' t} D {% C l6 d> Z4 垈 !LType Matrix Chart is the most basic and widely used matrix chart to compare only two data sets It is a form of upsidedown L When You Would Use an LType Matrix ChartBy reconstruction of q after the calculation of q d from , the coordinates of the force diagram are obtained as (4) x ∗ = L *1 C ∗ Qu y ∗ = L *1 C ∗ Qv where x ∗ and y ∗ v ∗ × 1 are the vertex coordinates of the force diagram, C ∗ v ∗ × e is the vertexedge incidence matrix representing the topology of the force diagram, Q e × e is the diagonal matrix of vector q, u and v e × 1 are the coordinate differences of the form diagram, and L ∗ = C ∗ C ∗ T is

R @ < C ?D "j _ y ?C GD wuu XO hoo J & C O c o ###O9 ӧ xhh Lf C)%*r S1 B gg2 " 306 f , = 3O M = Rvڶ { !X· (t)=Ax(t)Bu(t),y(t)=Cx(t)Du(t) (1) the observer is modeled as · xb(t)=Axb(t)Bu(t)Ly(t)−by(t), by(t)=Cbx(t)Du(t) (2) where Lis the n×mgain matrix for the observerR{ v mU q y Dt r= m 6 &Q &$$$$ J ( 0 0 e U g Q /^ ŋ ^ " < ' J / < Mek L&s 3 4 >۶/ u z W ~?

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F X → Y from a set X to a set Y associates to each x ∈ X a unique element f(x) ∈ Y Following is some commonly used terminologies 1 X is called the domain of f 2 Y is called the codomain of f 3 If f(x) = y, then we say y is the image of x The preimage of y is preimage(y) = {x ∈ X f(x) = y} 4The matrix diagram shows the relationship between two, three or four groups of information It also can give information about the relationship, such as its strength, the roles played by various individuals or measurements Six differently shaped matrices are possible L, T, Y, X, C and roofshaped, depending on how many groups must be compared • An Lshaped matrix relates two groups of items to each other (or one group to itself)The matrix diagram enables you to analyze relatively complex situations by exposing interactions and dependencies between things Six differently shaped matrices are commonly used L, T, Y, X, C and roofshaped Matrix Diagram Software Edraw allows you to draw Matrix in a fast and easy way You can directly use the premade template and input

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Step 1 Draw a spacetime diagram (see the The Paradox of Special Relativity page for a definition) from Vermilion's point of view For simplicity keep only one spatial dimension, the \(x\) direction, the direction of Cerulean's velocity relative to Vermilion The time \(t\) and distance \(x\) of events, relative to the origin, are those measured by VermilionThese are various types of Matrix Diagrams viz a) L Shape Matrix Diagram b) T c) Y d) X e) C L Shaped Matrix Diagram This is the most common type Example 1 A tyre manufacturing company was facing certain process defects They were interested in knowing the predominant defects of each group of tyres They prepared a L Matrix diagram to find that out Very Serious Bead defect Serious Carcass defect Not so serious Tread defect Curing defectWhere c j, the jth row of the output matrix C, determines the number of states that are observable by the output y j (t) 632 Observability of a DiscreteTime System Definition 632 The discretetime system (626) is said to be observable if there exists an index N such that the initial state x 0 can be completely determined from the knowledge of inputs u 0, u 1,, u N1, and the

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VI4 CHAPTER 6 THE LAGRANGIAN METHOD 62 The principle of stationary action Consider the quantity, S · Z t 2 t1 L(x;x;t_ )dt (614) S is called the actionIt is a quantity with the dimensions of (Energy)£(Time) S depends on L, and L in turn depends on the function x(t) via eq (61)4 Given any function x(t), we can produce the quantity SWe'll just deal with one coordinate, x, for nowPage 1 Matrix 122X Model Installation Guide NOTE This product is intended for installation by a professional installer only!Where c j, the jth row of the output matrix C, determines the number of states that are observable by the output y j (t) 632 Observability of a DiscreteTime System Definition 632 The discretetime system (626) is said to be observable if there exists an index N such that the initial state x 0 can be completely determined from the knowledge of inputs u 0, u 1,, u N1, and the

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XShaped Matrix Diagram This figure extends the Tshaped matrix example into an Xshaped matrix by including the relationships of freight lines with the manufacturing sites they serve and the customers who use them Each axis of the matrix is related to the two adjacent ones, but not to the one acrossSix differently shaped matrices are possible L, T, Y, X, C and roofshaped, depending on how many groups must be compared When to Use Each Matrix Diagram Shape In the examples, matrix axes have been shaded to emphasize the letter that gives each matrix its name An Lshaped matrix relates two groups of items to each other (or one group to itself)LShaped Matrix Diagram This Lshaped matrix summarizes customers' requirements The team placed numbers in the boxes to show numerical specifications and used check marks to show choice of packaging The Lshaped matrix actually forms an upsidedown L This is the most basic and most common matrix format Customer Requirements

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Models of the matrix The matrix type is chosen due to the number of groups of factors and the type of relationships / dependencies that occur between them There are different models of diagrams, they are marked with the letters L, T, Y, X, C Model L This is a basic model, it is used most oftenA T–shaped matrix relates three groups of items groups B and C are each related to A Groups B and C are not related to each other This Lshaped matrix summarizes customers' requirements The team placed numbers in the boxes to show numerical specifications and used check marks to show choice of packaging The Lshaped matrix actually forms an upsidedown L This is the most basic and most common matrix formatAny attempt to install this product by any person other than a trained professional may result in severe damage to a vehicle's electrical system and components

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L(x,y) = (x 2y, y 2x) and let S = {(2, 3), (1, 2)} be a basis for R 2 Find the matrix for L that sends a vector from the S basis to the standard basis Solution This involves two parts The first is to find the matrix for L from the standard basis to the standard basis This matrix is found by findingA LC A C L −=− T T TT Therefore, the gain matrix L can be computed using the RowReduced Echelon (RRE) method, Singular Value Decomposition (SVD), or the MATLAB place function in the same way as the control gain matrix K Tby replacing (, ) AB by (, ) AC TT By doing this, the result from any of these methods will give the matrixXShaped Matrix Diagram This figure extends the Tshaped matrix example into an Xshaped matrix by including the relationships of freight lines with the manufacturing sites they serve and the customers who use them Each axis of the matrix is related to the two adjacent ones, but not to the one across

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Matrix Diagram The Matrix Diagram shows the relationship between items At each intersection a relationship is either absent or present It then gives information about the relationship, such as its strength, the roles played by various individuals or measurements It can be shaped differently depending on how many groups must be compared Six differently shaped matrices are possible L, T, Y, X, C, R and roofshapedY (s) L s LC H(s) = X(s) = ³ 1s R 1 ´ 1 (43) 2 αs R 2C L LC where α denotes the ratio R 2/(R 1 R 2) The corresponding inputoutput differ­ ential equation is d2y(t) ³ 1 R 1 ´ dy(t) ³ 1 ´ ³ R 1 ´ dx(t) ³ 1 ´ α α y(t) = α α x(t) (44) dt2 R 2C L dt LC L dt LCThe matrix diagram shows the relationship between two, three, or four groups of information It also can give information about the relationship, such as its strength, of the roles played by various individuals or measurements Six differently shaped matrices are possible L, T, Y, X, C, and roofshaped, depending on how many groups must be compared

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The matrix diagram enables you to analyze relatively complex situations by exposing interactions and dependencies between things Six differently shaped matrices are possible L, T, Y, X, C, R and roofshaped, depending on how many groups must be compared Process decision program chartA T–shaped matrix relates three groups of items groups B and C are each related to A Groups B and C are not related to each other This Lshaped matrix summarizes customers' requirements The team placed numbers in the boxes to show numerical specifications and used check marks to show choice of packaging The Lshaped matrix actually forms an upsidedown L This is the most basic and most common matrix formatSix differently shaped matrices are possible L, T, Y, X, C and roofshaped, depending on how many groups must be compared When to Use Each Matrix Diagram Shape In the examples, matrix axes have been shaded to emphasize the letter that gives each matrix its name An Lshaped matrix relates two groups of items to each other (or one group to itself)

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The simple table of two dimensions (variables) is a simplest form of Matrix diagram Six differently shaped matrices are possible L, T, Y, X, C and roof–shaped, depending on how many groups must be compared The above example is Yshaped, where three groups of items are related with each others SQC team can use all these types of Matrix diagramRoof Shaped Matrix Diagram Six differently shaped matrices are possible L, T, Y, X, C, R and roofshaped, depending on how many groups must be compared" Seven Management and Planning Tools Wikipedia Use it to show what people and groups are involved in actions, and what their role is in every actionDescription This is a specific diagram with rows and columns that may come in several shapes L, T, Y, X, C & Roof that is used to find the strength of relationships among causes, objectives, and other factors Matrix Diagrams It belongs to the tool category Data representation

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Faces ¶ The faces are the complementary regions of the link diagram Each face is given as a list of corners of crossings as one goes around clockwiseThese corners are recorded as CrossingStrands, where CrossingStrand(c, j) denotes the corner of the face abutting crossing c between strand j and j 1Page 7 M M U U L L T T I I L L E E V V E E L L S S E E C C U U R R I I T T Y Y A A R R M M I I N N G Zone 1 It can also be used with Directed singlestage sensors The H1/6 blue instant trigger wire can also be used to shunt sensors during operation of auxiliary channels or remote startA Matrix Diagram shows the relationship between items At each intersection, a relationship is either absent or present It then gives information about the relationship, such as its strength, the roles played by various individuals or measurements It can be shaped differently depending on how many groups must be compared The other five differently shaped matrixes are L, T, Y, X, C and R

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DiL(t)/dt ¶ µ −αR 1/L −α/L ¶µ iL(t) ¶ µ 1/L ¶ dvC (t)/dt = α/C −1/(R 1 R 2)C vC (t) 0 v(t) (45) The use of matrix notation is a convenience;An Lshaped matrix relates two groups of items to each other (or one group to itself) A Tshaped matrix diagram relates three groups of items groups B and C are each related to A Groups B and C are not related to each other A Yshaped matrix relates three groups of itemsX(t) if L is correctly chosen Then, the output of the observer is the state estimate xˆ (t) The equation of the observer is xˆ& = Axˆ BuL(y −yˆ) or xˆ& =(A−LC)xˆ Bu Ly 1/s A B C 1/s A B C xˆ (t) yˆ (t) u (t) x (t) y (t) L ~y (t) Dynamical Observer xˆ (t) FullOrder Observer Plant Dynamics

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But remember that the Grand Tour works by rotating the dataset and then projecting it to 2D Combined, these two facts mean that as far as the Grand Tour is concerned, visualizing a vector x x x is the same as visualizing x U x U x U, and visualizing a vector x U Σ V T x U \Sigma V^T x U Σ V T is the same as visualizing x U Σ x U \Sigma x U ΣU e x )f !The matrix diagram shows the relationship between two, three or four groups of information It also can give information about the relationship, such as its strength, the roles played by various individuals or measurements Six differently shaped matrices are possible L, T, Y, X, C and roof–shaped, depending on how many groups must be compared

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The "Matrix Diagram Tool", which is one of seven new quality tools ,is used to analyze the collection data of the Six differently shaped matrices are possible L, T, Y, X, C and roofshaped,Matrices can be used in many ways to show relationships They can be shaped like an L, a T, an X, or a threedimensional, inverted Y The Lshaped matrix helps display relationships among any two different groups of people, processes, materials, machines, or environmental factors The Tshaped diagram is simply two Lshaped diagrams connected3 This is an nth order dynamical system, with initial stateˆx (0)equal to the initial estimate of the state The observer gain matrix L must be selected so that, even though the initial estimate xˆ (0) is not equal to the actual initial state x(0), as time passes the state estimate xˆ (t) converges to the actual state x(t)The quantity ~y(t) = y(t) −yˆ (t) is called theoutput estimation

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LShaped Matrix Diagram This Lshaped matrix summarizes customers' requirements The team placed numbers in the boxes to show numerical specifications and used check marks to show choice of packaging The Lshaped matrix actually forms an upsidedown L This is the most basic and most common matrix format Customer RequirementsL (1,0) = 1 t 2 = (1,0,1) L (0,1) = t t 2 = (0,1,1) hence the matrix is given by Now we will proceed with a more complicated example Example Let L be the linear transformation from R 2 to R 2 such that L (x,y) = (x 2y, y 2x) and let S = { (2, 3), (1, 2)} be a basis for R 2The simple table of two dimensions (variables) is a simplest form of Matrix diagram Six differently shaped matrices are possible L, T, Y, X, C and roof–shaped, depending on how many groups must be compared The above example is Yshaped, where three groups of items are related with each others SQC team can use all these types of Matrix diagram

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1 Draw your shape on graph paper Draw your shape on graph paper Different shapes of matrixes include L, T, Y, X, C and roofshaped The shape you choose depends on how many groups of data you wish to relate Lshaped matrixes are used for two groups Both the T and Y shapes are used to show three groups of information, but in a Tshaped matrix only one of the groups is related to both of the others, while in a Y shape the relationship between all three groups is shown

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