What does this matrix mean?Rotating Matrix by $180$ degrees through another matrixResult of multiplying a...
Is it possible for a character at any level to cast all 44 Cantrips in one week without Magic Items?
Need a non-volatile memory IC with near unlimited read/write operations capability
How did the IEC decide to create kibibytes?
Category-theoretic treatment of diffs, patches and merging?
Sense of humor in your sci-fi stories
Does the Wild Magic sorcerer's Tides of Chaos feature grant advantage on all attacks, or just the first one?
Did William Shakespeare hide things in his writings?
How do I explain that I don't want to maintain old projects?
Simple question about "vacuous truth".
Calculate the largest palindromic number from the product of two 6-digit numbers (100000 to 999999)
What does "spinning upon the shoals" mean?
What exactly is a "murder hobo"?
Why am I getting unevenly-spread results when using $RANDOM?
What is the shape of the upper boundary of water hitting a screen?
How can I reset Safari when Safari is broken?
Was it ever illegal to name a pig "Napoleon" in France?
How to evaluate the performance of open source solver?
Why did Robert F. Kennedy loathe Lyndon B. Johnson?
What was the significance of Spider-Man: Far From Home being an MCU Phase 3 film instead of a Phase 4 film?
Why SQL does not use the indexed view?
NOLOCK or Read Uncommitted locking / latching behaviours
Can we share mixing jug/beaker for developer, fixer and stop bath?
When do flights get cancelled due to fog?
What is the average number of draws it takes before you can not draw any more cards from the Deck of Many Things?
What does this matrix mean?
Rotating Matrix by $180$ degrees through another matrixResult of multiplying a scaling matrix with a rotation matrixWhat does it mean for $AA^T$ to be symmetric?What does “if the rightmost column of the augmented matrix contains a pivot then the system has no solutions” mean?What is the meaning of subtracting from the identity matrix?What does $u^T$ mean? How to compute this?What does the superscript $t$ in this matrix addition problem mean?Simplify this matrix exponentialHow to find the basis of this matrix?What does calculating the inverse of a matrix mean?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}
$begingroup$
$$
begin{bmatrix}
A\
aI
end{bmatrix}
$$
$a$ is some number is $I$ is the identity matrix. What does it mean when $A$ is on top of $aI$? What would be the resulting form?
linear-algebra
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
$endgroup$
add a comment |
$begingroup$
$$
begin{bmatrix}
A\
aI
end{bmatrix}
$$
$a$ is some number is $I$ is the identity matrix. What does it mean when $A$ is on top of $aI$? What would be the resulting form?
linear-algebra
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
$endgroup$
3
$begingroup$
It is a concatenation of matrices. It is formed by two matrices, one below the other. The number of columns of both need to be the same. The number of rows can be different.
$endgroup$
– Dunkel
8 hours ago
add a comment |
$begingroup$
$$
begin{bmatrix}
A\
aI
end{bmatrix}
$$
$a$ is some number is $I$ is the identity matrix. What does it mean when $A$ is on top of $aI$? What would be the resulting form?
linear-algebra
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
$endgroup$
$$
begin{bmatrix}
A\
aI
end{bmatrix}
$$
$a$ is some number is $I$ is the identity matrix. What does it mean when $A$ is on top of $aI$? What would be the resulting form?
linear-algebra
linear-algebra
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
asked 8 hours ago
Joshua LeungJoshua Leung
2032 silver badges8 bronze badges
2032 silver badges8 bronze badges
3
$begingroup$
It is a concatenation of matrices. It is formed by two matrices, one below the other. The number of columns of both need to be the same. The number of rows can be different.
$endgroup$
– Dunkel
8 hours ago
add a comment |
3
$begingroup$
It is a concatenation of matrices. It is formed by two matrices, one below the other. The number of columns of both need to be the same. The number of rows can be different.
$endgroup$
– Dunkel
8 hours ago
3
3
$begingroup$
It is a concatenation of matrices. It is formed by two matrices, one below the other. The number of columns of both need to be the same. The number of rows can be different.
$endgroup$
– Dunkel
8 hours ago
$begingroup$
It is a concatenation of matrices. It is formed by two matrices, one below the other. The number of columns of both need to be the same. The number of rows can be different.
$endgroup$
– Dunkel
8 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
That is an example of a block matrix. Let me give you an example. Consider for example the matrix $$A = begin{pmatrix}
1 & 2 \
3 & 4
end{pmatrix} .$$ Then we get $$begin{pmatrix}
A \
aI_2
end{pmatrix} = begin{pmatrix}
1 & 2 \
3 & 4 \
a & 0 \
0 & a
end{pmatrix}.$$
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
$endgroup$
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
add a comment |
$begingroup$
Just as Dunkel says in their comment, it represents a matrix concatenation. For example, if $$A=begin{bmatrix}1&2\3&4end{bmatrix}$$ and $a=5$ then we have $$begin{bmatrix}A\aIend{bmatrix}=begin{bmatrix}1&2\3&4\5&0\0&5end{bmatrix}$$ where I am using the $2times 2$ identity matrix.
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3284479%2fwhat-does-this-matrix-mean%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
That is an example of a block matrix. Let me give you an example. Consider for example the matrix $$A = begin{pmatrix}
1 & 2 \
3 & 4
end{pmatrix} .$$ Then we get $$begin{pmatrix}
A \
aI_2
end{pmatrix} = begin{pmatrix}
1 & 2 \
3 & 4 \
a & 0 \
0 & a
end{pmatrix}.$$
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
$endgroup$
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
add a comment |
$begingroup$
That is an example of a block matrix. Let me give you an example. Consider for example the matrix $$A = begin{pmatrix}
1 & 2 \
3 & 4
end{pmatrix} .$$ Then we get $$begin{pmatrix}
A \
aI_2
end{pmatrix} = begin{pmatrix}
1 & 2 \
3 & 4 \
a & 0 \
0 & a
end{pmatrix}.$$
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
$endgroup$
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
add a comment |
$begingroup$
That is an example of a block matrix. Let me give you an example. Consider for example the matrix $$A = begin{pmatrix}
1 & 2 \
3 & 4
end{pmatrix} .$$ Then we get $$begin{pmatrix}
A \
aI_2
end{pmatrix} = begin{pmatrix}
1 & 2 \
3 & 4 \
a & 0 \
0 & a
end{pmatrix}.$$
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
$endgroup$
That is an example of a block matrix. Let me give you an example. Consider for example the matrix $$A = begin{pmatrix}
1 & 2 \
3 & 4
end{pmatrix} .$$ Then we get $$begin{pmatrix}
A \
aI_2
end{pmatrix} = begin{pmatrix}
1 & 2 \
3 & 4 \
a & 0 \
0 & a
end{pmatrix}.$$
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
edited 8 hours ago
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
answered 8 hours ago
ThorWittichThorWittich
2,7092 silver badges17 bronze badges
2,7092 silver badges17 bronze badges
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
add a comment |
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
That's pretty funny how we chose the same $A$ matrix for our example.
$endgroup$
– Dave
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
$begingroup$
Indeed! Very canonical matrix haha.
$endgroup$
– ThorWittich
8 hours ago
add a comment |
$begingroup$
Just as Dunkel says in their comment, it represents a matrix concatenation. For example, if $$A=begin{bmatrix}1&2\3&4end{bmatrix}$$ and $a=5$ then we have $$begin{bmatrix}A\aIend{bmatrix}=begin{bmatrix}1&2\3&4\5&0\0&5end{bmatrix}$$ where I am using the $2times 2$ identity matrix.
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
$endgroup$
add a comment |
$begingroup$
Just as Dunkel says in their comment, it represents a matrix concatenation. For example, if $$A=begin{bmatrix}1&2\3&4end{bmatrix}$$ and $a=5$ then we have $$begin{bmatrix}A\aIend{bmatrix}=begin{bmatrix}1&2\3&4\5&0\0&5end{bmatrix}$$ where I am using the $2times 2$ identity matrix.
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
$endgroup$
add a comment |
$begingroup$
Just as Dunkel says in their comment, it represents a matrix concatenation. For example, if $$A=begin{bmatrix}1&2\3&4end{bmatrix}$$ and $a=5$ then we have $$begin{bmatrix}A\aIend{bmatrix}=begin{bmatrix}1&2\3&4\5&0\0&5end{bmatrix}$$ where I am using the $2times 2$ identity matrix.
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
$endgroup$
Just as Dunkel says in their comment, it represents a matrix concatenation. For example, if $$A=begin{bmatrix}1&2\3&4end{bmatrix}$$ and $a=5$ then we have $$begin{bmatrix}A\aIend{bmatrix}=begin{bmatrix}1&2\3&4\5&0\0&5end{bmatrix}$$ where I am using the $2times 2$ identity matrix.
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
answered 8 hours ago
DaveDave
9,6921 gold badge11 silver badges33 bronze badges
9,6921 gold badge11 silver badges33 bronze badges
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3284479%2fwhat-does-this-matrix-mean%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
3
$begingroup$
It is a concatenation of matrices. It is formed by two matrices, one below the other. The number of columns of both need to be the same. The number of rows can be different.
$endgroup$
– Dunkel
8 hours ago