###### Asked in Toyota MatrixPronounsLinear Algebra

Toyota Matrix

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Linear Algebra

# What is the order of the set of all circulant matrices?

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## Related Questions

###### Asked in Algebra, Senior Secondary Certificate SSC, HSC Maharashtra Board , Abstract Algebra

### Is the set of all 2x2 invertible matrices a subspace of all 2x2 matrices?

I assume since you're asking if 2x2 invertible matrices are a
"subspace" that you are considering the set of all 2x2 matrices as
a vector space (which it certainly is).
In order for the set of 2x2 invertible matrices to be a subspace
of the set of all 2x2 matrices, it must be closed under addition
and scalar multiplication.
A 2x2 matrix is invertible if and only if its determinant is
nonzero. When multiplied by a scalar (let's call it c), the
determinant of a 2x2 matrix will be multiplied by c^2 since the
determinant is linear in each row (two rows -> two factors of
c). If the determinant was nonzero to begin with c^2 times the
determinant will be nonzero, so an invertible matrix multiplied by
a scalar will remain invertible. Therefore the set of all 2x2
invertible matrices is closed under scalar multiplication.
However, this set is not closed under addition. Consider the
matrices {[1 0], [0 1]} and {[-1 0], [0 -1]}. Both are invertible
(in this case, they are both their own inverses). However, their
sum is {[0 0], [0 0]}, which is not invertible because its
determinant is 0.
In conclusion, the set of invertible 2x2 matrices is not a
subspace of the set of all 2x2 matrices because it is not closed
under addition.

###### Asked in Math and Arithmetic, Physics

### Why you say matercis is vector?

In math, a "vector field" is an abstract term for a set, and a
number of operations, that have specific properties. Matrices of
the same size, for example, all 3 x 2 matrices, combined with
matrix addition and multiplication by a scalar, happens to have all
those properties. You may want to read an introductory Linear
Algebra book for more details.

###### Asked in Abstract Algebra

### What is the raven standard progressive matrices?

Raven
Standard Progressive Matrices: These were the original form of
the matrices, first published in 1938. The booklet comprises five
sets (A to E) of 12 items each (e.g., A1 through A12), with items
within a set becoming increasingly difficult, requiring ever
greater cognitive capacity to encode and analyze information. All
items are presented in black ink on a white background

###### Asked in Algebra, Abstract Algebra, Linear Algebra

### How matrices used in engineering?

If you have a system, which can be expressed as a set of linear
equations, then you can utilize matrices to help solve it. One
example is an electrical circuit which uses linear devices (example
are constant voltage sources and resistive loads). To find the
current through each device, a set of linear equations is
derived.

###### Asked in Electrical Engineering, Linear Algebra

### What are the applications of matrices in electrical engineering?

Matrices can be used for circuit analysis because a circuit
component can have an impedance matrix, an admittance matrix or a
scattering matrix, of order equal to the number of ports the
circuit has. This can also be used for antenna arrays when you have
an antenna circuit connected to a feeder (transmission-line)
circuit.
Matrices are also used in the numerical solution of linear
equations: when you have a system of N equations it needs matrices
of order N.
In field theory integral equations arise which can be solved
numerically by using a piecewise-linear approximation which turns
an integral equation into a set of linear equations. This is used
for analysing raio antennas using the method of moments.
All the above applications are coded into software which can be
bought and used but designing the sotware falls inside the remit of
electrical engineering.

###### Asked in Typography

### What was the design process for Adobe Garamond Pro?

When you bought text-size type in the really old days, you got a
rack of molds called "matrices" and cast your own type blocks--type
was made from lead and wore out quickly, so to protect your
investment you'd make type as you needed it. Matrices were made by
people called punch cutters. One of the more prolific punch cutters
was a Frenchman named Claude Garamond (at one time he spelled it
Garamont). He sold matrices to printers, but he wasn't a printer
himself...until he got stupid and went into the printing business.
All his customers were printers; now he's competing against them,
and they told him what they thought of that idea by halting their
purchases of Garamond matrices. End result: Claude Garamond died
broke and drunk and is buried in a pauper's grave. Okay, back to
the original discussion...the world possesses one set of matrices
made by Claude Garamond. It is in the Plantin-Moretus Museum in
Antwerp, Belgium. Adobe Garamond's genesis is rubbings from that
set of matrices.

###### Asked in Statistics, How To

### How to find the median?

###### Asked in Algebra

### What is an algebraic structure?

###### Asked in Math and Arithmetic, Abstract Algebra

### Do matrices form an abelian group under multiplication?

More precisely, I think you're asking whether the set of n X n
matrices forms an abelian group under multiplication. The answer is
no (assuming n>1). For example
(1 0)(0 1) = (0 1)
(0 0)(0 0) (0 0),
but
(0 1)(1 0) = (0 0)
(0 0)(0 0) (0 0). However, the set of n x n diagonal
matrices does form an Abelian set. This is true regardless of the
direction of the diagonality, right-to-left or left-to-right. Note
that the resulting matrix will also be diagonal, but always
right-to-left.

###### Asked in Management and Supervision

### What is performance matrices?

A performance matrices is a set of tables containing data on
system functions grouped together by function ie, logon, edit,
create etc., usually the system is loaded down and perfomance
related information ie, CPU usage, bandwidth, time to complete
function etc., is collected and used to scale up or down and
identify critical (and non critical) system performance issues.
Generally it will depend upon the system requirements for how the
matrices will be set up. ie If the company has a target requirement
10 secs for logon to the system then you would load the system down
and the colleted information will show how close they are to this
target.

###### Asked in Custody, Children and the Law, Child Support

### Do I still have to pay child support on an 18 year old child who is still in school but has moved in with her boyfriend?

You need to review your child support order. Your obligations
are set forth in the order.
You need to review your child support order. Your obligations are
set forth in the order.
You need to review your child support order. Your obligations are
set forth in the order.
You need to review your child support order. Your obligations are
set forth in the order.

###### Asked in Math and Arithmetic, Algebra

### What is closed under subtraction?

The set of all integers;
the set of all rational numbers;
the set of all real numbers;
the set of all complex numbers.
Also their multiples - for example
the set of all multiples of 2;
the set of all multiples of 2.5;
the set of all multiples of sqrt(17);
the set of all multiples of 3 + 4i where i is the imaginary
square root of -1.

###### Asked in Math and Arithmetic

### Does the ring of full rank square matrices form a domain?

It would form a domain, except that it fails to even be a ring.
The 0 matrix has rank 0, so it is never a full rank matrix -
therefore the set of full rank square matrices doesn't have an
additive identity. It is true that there are no zero divisors among
the full rank square matrices: if AB=0, and A has full rank, then
it's invertible, so A-1AB=A-10, or B=0. Similarly, if BA=0,
BAA-1=0A-1 so B=0.